Invention Archive · Daily Research Session

Invention Archive · Daily Research Session #73

Workflow file for this run

.github/workflows/daily_invention_archive.yml at 634f434

	name: Invention Archive · Daily Research Session

	# ──────────────────────────────────────────────────────────────────────────────
	# Runs once per day at 07:00 UTC.
	#
	# Scans all constructs in constructs/ dynamically, then performs a
	# mathematically rigorous cross-construct analysis. Seven analysis topics
	# rotate by day-of-year mod 7. No LLM. No external API. Pure mathematics.
	#
	# T0 Information-Theoretic Construct Topology
	# Jaccard similarity matrix over tag vectors; graph clustering coefficient;
	# nearest-neighbor structure in tag space.
	#
	# T1 Harmonic Series & Wave Interference Analysis
	# For resonance-based constructs (HRF, FRAE, AetherSPARC, SpectraNova,
	# HagMoE): harmonic overtone series, resonant pairs, spectral entropy,
	# Shannon channel capacity of harmonic channels.
	#
	# T2 Genomic Information Theory
	# For longevity constructs (AION, EternaSeq, EternaHeart): Shannon entropy
	# of DNA alphabet, Hayflick information loss, Landauer erasure cost of
	# epigenetic reprogramming, genetic code redundancy bounds.
	#
	# T3 Evolutionary Dynamics & Dual-State Stability
	# For GENEVO, BSHDER, Cytomorphic: Fisher's fundamental theorem (verified
	# numerically), Eigen error threshold, dual-state information differential.
	#
	# T4 High-Dimensional Geometry
	# For HRF-26D and GOD optimizer: unit hypersphere volume, Johnson-
	# Lindenstrauss bounds, concentration of measure, curse of dimensionality.
	#
	# T5 Cross-Paradigm Formal Bridges
	# Explicit mathematical isomorphisms between constructs: HRF↔NECF,
	# BSHDER↔H[L], GENEVO↔epistemic contagion, AION↔Landauer.
	#
	# T6 Spectral Decomposition & Encoding Capacity
	# For SpectraNova, FRAE, AetherSPARC: FFT decomposition of synthetic
	# multi-component signal, per-component SNR, Shannon-Hartley encoding
	# capacity per frequency bin.
	# ──────────────────────────────────────────────────────────────────────────────

	on:
	schedule:
	- cron: '0 7 * * *'
	workflow_dispatch:

	concurrency:
	group: invention-archive-daily
	cancel-in-progress: false

	permissions:
	contents: write

	jobs:
	daily-session:
	name: Compute · Analyse · Commit
	runs-on: ubuntu-latest

	steps:

	- name: Checkout
	uses: actions/checkout@v4
	with:
	fetch-depth: 1

	- name: Set up Python 3.11
	uses: actions/setup-python@v5
	with:
	python-version: '3.11'

	- name: Install dependencies
	run: pip install --quiet "numpy>=1.24" "scipy>=1.11"

	- name: Run daily analysis
	shell: python3 {0}
	run: \|
	import numpy as np
	from scipy.stats import linregress
	from scipy.signal import find_peaks
	from datetime import date
	import os, json, textwrap, math

	# ── Date / seed / topic ─────────────────────────────────────────────
	today = date.today()
	DATE_STR = today.strftime("%Y-%m-%d")
	SEED = int(today.strftime("%Y%m%d"))
	DOY = today.timetuple().tm_yday
	TOPIC_IDX = (DOY - 1) % 7
	SESSION_ID = f"IA-{today.year}-{DOY:03d}-T{TOPIC_IDX}"
	rng = np.random.default_rng(SEED)

	# ── Known construct catalog (fallback when files are sparse) ────────
	# Updated as new constructs are added to the repo.
	KNOWN_CONSTRUCTS = {
	"HRF": {"full": "Harmonic Resonance Forest",
	"domain": "resonance",
	"tags": ["resonance","wave","hierarchical","ai",
	"forest","harmonic","26d"],
	"dims": 26},
	"BSHDER": {"full": "Bionic Self-Healing Dual-state Encoder",
	"domain": "neural",
	"tags": ["self-healing","neural","bionic","dna",
	"fragile","protected","dual-state"],
	"dims": None},
	"GENEVO": {"full": "Genetic Evolutionary Organoid",
	"domain": "evolutionary",
	"tags": ["evolution","gradient","organoid",
	"genetic","self-evolving"],
	"dims": None},
	"FRAE": {"full": "Frequency-Resonance Adaptive Encoder",
	"domain": "resonance",
	"tags": ["frequency","resonance","encoding",
	"specialized"],
	"dims": None},
	"Cytomorphic": {"full": "Cytomorphic Architecture",
	"domain": "biology",
	"tags": ["cellular","biology","neural",
	"structural","biomimetic"],
	"dims": None},
	"NECF": {"full": "Non-Equilibrium Cognitive Field",
	"domain": "physics",
	"tags": ["thermodynamics","non-equilibrium",
	"oscillator","identity","field"],
	"dims": None},
	"HagMoE": {"full": "Harmonic-Augmented Gating Mixture of Experts",
	"domain": "resonance",
	"tags": ["harmonic","mixture-of-experts",
	"gating","augmented"],
	"dims": None},
	"DeathRay": {"full": "Death Ray Sniper Correction Layer",
	"domain": "optimization",
	"tags": ["correction","precision","systematic-error",
	"foundation-model"],
	"dims": None},
	"GOD": {"full": "General Omni Dimensional Optimizer",
	"domain": "optimization",
	"tags": ["optimizer","26d","dimensional",
	"dynamic","selection"],
	"dims": 26},
	"LIM": {"full": "Latent Inference Manifold",
	"domain": "latent",
	"tags": ["latent","inference","manifold",
	"stabilization"],
	"dims": None},
	"LCM": {"full": "Latent Consensus Manifold",
	"domain": "latent",
	"tags": ["latent","consensus","manifold",
	"reasoning"],
	"dims": None},
	"AION": {"full": "Algorithmic Inversion of genomic Noise",
	"domain": "longevity",
	"tags": ["genomic","entropy","aging","reversal",
	"biological-clock"],
	"dims": None},
	"HSU": {"full": "Holographic Soul Unit",
	"domain": "longevity",
	"tags": ["holographic","soul","kernel","periodic",
	"resonance","biological"],
	"dims": None},
	"EternaSeq": {"full": "EternaSeq Genomic Sequencer",
	"domain": "longevity",
	"tags": ["genomic","sequencing","longevity",
	"cardiovascular"],
	"dims": None},
	"EternaHeart": {"full": "EternaHeart Cardiovascular Longevity Model",
	"domain": "longevity",
	"tags": ["cardiovascular","longevity","genomic"],
	"dims": None},
	"NanoCortex": {"full": "NanoCortex Biological Signal Processor",
	"domain": "biology",
	"tags": ["nanoscale","biological-signal",
	"high-resolution"],
	"dims": None},
	"AetherSPARC": {"full": "Aether Signal Processing and Resonance Coder",
	"domain": "resonance",
	"tags": ["signal-processing","resonance",
	"coding","physics"],
	"dims": None},
	"SpectraNova": {"full": "SpectraNova Spectral Decomposer",
	"domain": "resonance",
	"tags": ["spectral","decomposition","signal",
	"analysis"],
	"dims": None},
	"MateriaMind": {"full": "MateriaMind Materials-Inspired Architecture",
	"domain": "physics",
	"tags": ["materials","neural","configuration",
	"physics"],
	"dims": None},
	}

	# ── Read actual constructs from repo ────────────────────────────────
	repo_constructs = {}
	constructs_dir = "constructs"
	if os.path.isdir(constructs_dir):
	for entry in sorted(os.listdir(constructs_dir)):
	meta_path = os.path.join(constructs_dir, entry, "metadata.json")
	if os.path.exists(meta_path):
	try:
	with open(meta_path) as f:
	meta = json.load(f)
	name = meta.get("name", entry)
	repo_constructs[name] = meta
	except Exception:
	pass

	# Merge: repo data overrides catalog defaults
	constructs = dict(KNOWN_CONSTRUCTS)
	for name, meta in repo_constructs.items():
	if name in constructs:
	constructs[name]["status"] = meta.get("status", "active")
	constructs[name]["created"] = meta.get("created", "unknown")
	else:
	constructs[name] = {
	"full": meta.get("full_name", name),
	"domain": meta.get("type", "unknown"),
	"tags": meta.get("tags", []),
	"dims": None,
	}

	N_CONSTRUCTS = len(constructs)
	names = list(constructs.keys())

	# ── Topic titles ───────────────────────────────────────────────────
	TITLES = [
	"Information-Theoretic Construct Topology: Jaccard Similarity "
	"Matrix and Graph Clustering Coefficient",
	"Harmonic Series and Wave Interference Analysis: Resonant "
	"Pairs, Spectral Entropy, and Channel Capacity",
	"Genomic Information Theory: Shannon Entropy Bounds, Hayflick "
	"Information Loss, and Landauer Erasure Cost",
	"Evolutionary Dynamics and Dual-State Stability: Fisher's "
	"Fundamental Theorem and Eigen Error Threshold",
	"High-Dimensional Geometry: Hypersphere Volume, "
	"Johnson-Lindenstrauss Bounds, Concentration of Measure",
	"Cross-Paradigm Formal Bridges: Mathematical Isomorphisms "
	"Between Resonance, Field, Evolutionary, and Longevity Constructs",
	"Spectral Decomposition and Encoding Capacity: FFT Analysis, "
	"Per-Component SNR, and Shannon-Hartley Bounds",
	]
	SLUGS = [
	"construct_topology",
	"harmonic_interference",
	"genomic_information_theory",
	"evolutionary_dynamics",
	"high_dimensional_geometry",
	"cross_paradigm_bridges",
	"spectral_encoding_capacity",
	]
	TITLE = TITLES[TOPIC_IDX]
	SLUG = SLUGS[TOPIC_IDX]

	# ════════════════════════════════════════════════════════════════════
	# TOPIC FUNCTIONS
	# ════════════════════════════════════════════════════════════════════

	def topic_0_topology():
	"""Information-theoretic topology of the construct graph."""
	all_tags = sorted(set(t for c in constructs.values()
	for t in c.get("tags", [])))
	tag_idx = {t: i for i, t in enumerate(all_tags)}
	D = len(all_tags)

	M = np.zeros((N_CONSTRUCTS, D))
	for i, name in enumerate(names):
	for tag in constructs[name].get("tags", []):
	if tag in tag_idx:
	M[i, tag_idx[tag]] = 1.0

	def jaccard(a, b):
	inter = np.sum(np.minimum(a, b))
	union = np.sum(np.maximum(a, b))
	return float(inter / union) if union > 0 else 0.0

	S = np.array([[jaccard(M[i], M[j])
	for j in range(N_CONSTRUCTS)]
	for i in range(N_CONSTRUCTS)])

	# Top pairs
	pairs = sorted(
	[(S[i,j], names[i], names[j])
	for i in range(N_CONSTRUCTS)
	for j in range(i+1, N_CONSTRUCTS)],
	reverse=True,
	)

	# Graph properties at threshold 0.12
	thresh = 0.12
	adj = (S > thresh).astype(float)
	np.fill_diagonal(adj, 0)
	k = adj.sum(axis=1)
	A3 = np.linalg.matrix_power(adj, 3)
	triangles = np.trace(A3) / 6.0
	possible = np.sum(k * (k - 1)) / 2.0
	CC = float(triangles / possible) if possible > 0 else 0.0
	mean_deg = float(k.mean())
	n_isolated = int((k == 0).sum())

	# Degree entropy (diversity of connections)
	k_norm = k / (k.sum() + 1e-10)
	H_deg = float(-np.sum(k_norm[k_norm > 0] * np.log2(k_norm[k_norm > 0])))

	top5_rows = ""
	for s, a, b in pairs[:5]:
	ca = constructs[a]['full'][:28]
	cb = constructs[b]['full'][:28]
	top5_rows += f"\| {a} \| {b} \| {s:.4f} \|\n"

	commit_suffix = (f"N={N_CONSTRUCTS} CC={CC:.4f} "
	f"top_pair={pairs[0][1]}/{pairs[0][2]} "
	f"J={pairs[0][0]:.4f}")

	doc = rf"""--
	session_id: {SESSION_ID}
	date: {DATE_STR}
	topic: Construct Topology
	constructs_present: {N_CONSTRUCTS}
	seed: {SEED}
	---

	# Invention Archive — Daily Session {DATE_STR}

	Session ID: `{SESSION_ID}`
	Topic: {TITLE}

	---

	## 1. Method

	Each construct in the archive is represented as a binary vector
	$\mathbf{{v}}_i \in \{{0,1\}}^D$ over a shared tag vocabulary of
	$D = {D}$ terms. The pairwise Jaccard similarity is

	$$J(i,j) = \frac{{\|\mathbf{{v}}_i \cap \mathbf{{v}}_j\|}}{{\|\mathbf{{v}}_i \cup \mathbf{{v}}_j\|}}$$

	A construct graph $G = (V, E)$ is formed by thresholding at $J > {thresh}$.
	The clustering coefficient $C = T / P$ where $T$ is the number of
	closed triangles and $P$ is the number of connected triples measures the
	tendency of related constructs to form cohesive clusters.

	---

	## 2. Results — {today.strftime('%B %d, %Y')}

	Archive state: {N_CONSTRUCTS} constructs · {D} distinct tags

	### 2.1 Top Pairwise Similarities

	\| Construct A \| Construct B \| J(A,B) \|
	\|---\|---\|:---:\|
	{top5_rows.strip()}

	### 2.2 Graph Statistics (threshold J > {thresh})

	\| Metric \| Value \|
	\|---\|---\|
	\| Constructs (nodes) \| {N_CONSTRUCTS} \|
	\| Tag vocabulary size \| {D} \|
	\| Mean degree \| {mean_deg:.3f} \|
	\| Clustering coefficient \| {CC:.5f} \|
	\| Isolated constructs \| {n_isolated} \|
	\| Degree entropy \| {H_deg:.4f} bits \|

	---

	## 3. Interpretation

	The clustering coefficient $C = {CC:.5f}$ indicates that the construct
	graph is currently
	{'sparsely connected — constructs operate in largely independent domains' if CC < 0.1 else 'moderately clustered — several domain cohorts are forming' if CC < 0.4 else 'highly clustered — strong inter-domain coupling'}.
	The most similar pair is {pairs[0][1]} and {pairs[0][2]}
	($J = {pairs[0][0]:.4f}$), consistent with their shared tags.
	The degree entropy $H = {H_deg:.4f}$ bits characterises the heterogeneity
	of construct connectivity; as the archive grows, this is expected to
	increase toward $\log_2(N) = {np.log2(N_CONSTRUCTS):.3f}$ bits.

	---
	{SESSION_ID} · {DATE_STR} · seed {SEED}
	"""
	return doc.strip(), commit_suffix

	# ──────────────────────────────────────────────────────────────────

	def topic_1_harmonic():
	"""Harmonic series and wave interference for resonance constructs."""
	res_constructs = {k: v for k, v in constructs.items()
	if v.get("domain") == "resonance"
	or k in ("HRF","FRAE","AetherSPARC",
	"SpectraNova","HagMoE")}

	d = constructs.get("HRF", {}).get("dims", 26) or 26
	f0 = 1.0
	freqs = np.array([f0 * (k + 1) for k in range(d)])

	# Spectral entropy of 1/f (pink noise) weight distribution
	amp = 1.0 / np.arange(1, d + 1)
	amp /= amp.sum()
	H_spec = float(-np.sum(amp * np.log2(amp + 1e-15)))
	H_max = float(np.log2(d))
	eff_pct = 100.0 * H_spec / H_max

	# Resonant pairs: freq ratio p/q with denominator <= 8
	from fractions import Fraction
	resonant = []
	for i in range(d):
	for j in range(i + 1, d):
	ratio = freqs[i] / freqs[j]
	frac = Fraction(ratio).limit_denominator(8)
	if abs(float(frac) - ratio) < 0.02:
	resonant.append((i + 1, j + 1,
	frac.numerator, frac.denominator))
	n_resonant = len(resonant)

	# Shannon channel capacity: C = B*log2(1+SNR)
	B_total = float(freqs.sum())
	SNR_db = float(15.0 + rng.uniform(-3, 3))
	SNR_lin = 10 ** (SNR_db / 10.0)
	C_chan = B_total * np.log2(1.0 + SNR_lin)

	# Beat frequencies: closest pair
	beat_mat = np.abs(freqs[:, np.newaxis] - freqs[np.newaxis, :])
	np.fill_diagonal(beat_mat, np.inf)
	min_beat = float(beat_mat.min())

	# Expected angle between random unit vectors in d dimensions
	expected_cos = float(np.sqrt(2.0 / (np.pi * d)))
	expected_deg = float(np.degrees(np.arccos(np.clip(expected_cos, -1, 1))))

	res_list = "\n".join(f"- {k}: {v['full']}"
	for k, v in res_constructs.items())

	commit_suffix = (f"d={d} H_spec={H_spec:.4f}/{H_max:.4f} "
	f"resonant_pairs={n_resonant} "
	f"C={C_chan:.1f}bits SNR={SNR_db:.1f}dB")

	doc = rf"""--
	session_id: {SESSION_ID}
	date: {DATE_STR}
	topic: Harmonic Interference
	seed: {SEED}
	HRF_dimensions: {d}
	---

	# Invention Archive — Daily Session {DATE_STR}

	Session ID: `{SESSION_ID}`
	Topic: {TITLE}

	---

	## 1. Resonance-Domain Constructs

	{res_list}

	---

	## 2. Harmonic Series — HRF {d}-Dimensional Substrate

	The Harmonic Resonance Forest models each of its $d = {d}$ dimensions as an
	oscillator tuned to a harmonic of the fundamental $f_0 = {f0:.4f}$:

	$$f_k = k \cdot f_0, \quad k = 1, 2, \ldots, {d}$$

	### 2.1 Spectral Weight Distribution

	Under a $1/f$ (pink noise) amplitude weighting $A_k = 1/k$ (normalised):

	$$H_{{\rm spec}} = -\sum_{{k=1}}^{{{d}}} A_k \log_2 A_k = {H_spec:.5f} \text{{ bits}}$$

	compared with the uniform maximum $\log_2 {d} = {H_max:.5f}$ bits.
	The spectral efficiency is $\eta = {eff_pct:.2f}\%$.

	### 2.2 Resonant Dimension Pairs

	Two dimensions $i, j$ are resonant when their frequency ratio is a
	simple rational $p/q$ with $q \leq 8$ (within 2% tolerance):

	$$\frac{{f_i}}{{f_j}} \approx \frac{{p}}{{q}}, \quad q \leq 8$$

	In $d = {d}$ dimensions: {n_resonant} resonant pairs detected.
	First five: {', '.join(f'dim{a}/{b}={p}/{q}' for a,b,p,q in resonant[:5])}.

	### 2.3 Shannon Channel Capacity

	Treating the harmonic series as a multi-channel communication system with
	total bandwidth $B = \sum_k f_k = {B_total:.2f}$ (normalised units) and
	SNR $= {SNR_db:.2f}$ dB:

	$$C = B \cdot \log_2(1 + \text{{SNR}}) = {B_total:.2f} \cdot \log_2(1 + {SNR_lin:.1f}) = {C_chan:.2f} \text{{ bits/s}}$$

	### 2.4 Minimum Beat Frequency

	$$\Delta f_{{\rm min}} = \min_{{i \neq j}} \|f_i - f_j\| = {min_beat:.4f}$$

	### 2.5 Angular Geometry of Harmonic Dimensions

	In $d = {d}$ dimensions, the expected angle between two random unit vectors is:

	$$\mathbb{{E}}[\cos\theta] = \sqrt{{\frac{{2}}{{\pi d}}}} = {expected_cos:.5f}
	\implies \mathbb{{E}}[\theta] \approx {expected_deg:.2f}^\circ$$

	Dimensions are near-orthogonal, confirming the representational independence
	assumption underlying HRF's hierarchical decomposition.

	---

	## 3. Interpretation

	The $1/f$ spectral weighting achieves {eff_pct:.1f}% of maximum entropy,
	consistent with efficient natural coding (Field, 1987). With {n_resonant}
	resonant dimension pairs, HRF's 26D space contains substantial harmonic
	structure — these pairs can exhibit constructive interference, creating
	emergent higher-level representations from simpler harmonic components.

	---
	{SESSION_ID} · {DATE_STR} · seed {SEED}
	"""
	return doc.strip(), commit_suffix

	# ──────────────────────────────────────────────────────────────────

	def topic_2_genomic():
	"""Genomic information theory for longevity constructs."""
	# DNA base frequencies (human genome average)
	bases = np.array([0.295, 0.295, 0.205, 0.205])
	H_DNA = float(-np.sum(bases * np.log2(bases + 1e-15)))
	H_DNA_max= 2.0
	G = 3.2e9 # base pairs

	I_genome = G * H_DNA
	coding_frac = 0.015
	I_coding = I_genome * coding_frac

	# Somatic mutation rate (Alexandrov et al. 2013)
	mu_rate = float(1.3 + rng.uniform(-0.1, 0.1))
	H_loss_div = mu_rate * np.log2(G)

	# Hayflick limit telomere analysis
	hayflick = 50
	telomere_bp_loss = 50 # base pairs per division
	telomere_length = 15000
	H_telomere_lost = hayflick * telomere_bp_loss * H_DNA

	# Landauer erasure cost at body temperature
	kB = 1.380649e-23
	T_body = 310.0
	E_per_bit = kB * T_body * math.log(2)
	E_reprog = H_telomere_lost * E_per_bit
	ATP_per_mol = 30.5e3
	avogadro = 6.022e23
	n_ATP = E_reprog / (ATP_per_mol / avogadro)

	# Genetic code redundancy: 64 codons, 20 amino acids
	code_redundancy = math.log2(64) - math.log2(20)

	# AION target: fractional information recovery
	aion_target_pct = float(85.0 + rng.uniform(-5, 5))
	H_recover = H_telomere_lost * aion_target_pct / 100.0
	E_aion = H_recover * E_per_bit

	commit_suffix = (f"H_DNA={H_DNA:.5f}bpb "
	f"H_telomere={H_telomere_lost:.1f}bits "
	f"E_reprog={E_reprog:.3e}J "
	f"n_ATP={n_ATP:.2e}")

	doc = rf"""--
	session_id: {SESSION_ID}
	date: {DATE_STR}
	topic: Genomic Information Theory
	seed: {SEED}
	---

	# Invention Archive — Daily Session {DATE_STR}

	Session ID: `{SESSION_ID}`
	Topic: {TITLE}

	---

	## 1. Constructs — Longevity Domain

	- AION: Algorithmic reversal of genomic entropy (biological clock)
	- EternaSeq: Genomic sequencing for longevity
	- EternaHeart: Cardiovascular longevity modelling
	- HSU: Holographic Soul Unit — non-monotonic kernel analysis

	---

	## 2. Shannon Entropy of the DNA Alphabet

	With empirical base frequencies $(f_A, f_T, f_G, f_C) =
	({bases[0]:.3f}, {bases[1]:.3f}, {bases[2]:.3f}, {bases[3]:.3f})$:

	$$H_{{\rm DNA}} = -\sum_b f_b \log_2 f_b = {H_DNA:.5f} \text{{ bits/base}}$$

	versus the theoretical maximum $\log_2 4 = 2.0000$ bits/base for a uniform
	alphabet. The human genome ($G = 3.2 \times 10^9$ bases) carries:

	$$I_{{\rm genome}} = G \cdot H_{{\rm DNA}} = {I_genome/1e9:.3f} \text{{ Gbits}}$$

	of which approximately $f_{{\rm coding}} = {coding_frac:.1%}$ is protein-coding:

	$$I_{{\rm coding}} = {I_coding/1e6:.2f} \text{{ Mbits}}$$

	---

	## 3. Information Loss Rate

	The somatic mutation rate is approximately $\mu \approx {mu_rate:.2f}$
	substitutions per cell division (Alexandrov et al., 2013). Each substitution
	destroys $\log_2 G$ bits of positional information:

	$$\Delta I_{{\rm div}} = \mu \cdot \log_2 G = {mu_rate:.2f} \times {np.log2(G):.3f} = {H_loss_div:.3f} \text{{ bits/division}}$$

	---

	## 4. Hayflick Limit — Telomere Information Budget

	Over $n_H = {hayflick}$ cell divisions (Hayflick limit), telomeres shorten
	by $\approx {telomere_bp_loss}$ bp/division from an initial length of
	${telomere_length}$ bp. Total telomere information erased:

	$$\Delta I_{{\rm telomere}} = n_H \cdot \ell_{{\rm loss}} \cdot H_{{\rm DNA}}
	= {hayflick} \times {telomere_bp_loss} \times {H_DNA:.5f}
	= {H_telomere_lost:.3f} \text{{ bits}}$$

	---

	## 5. Landauer Cost of AION Reversal

	Landauer's principle sets the minimum thermodynamic cost of erasing one bit
	at temperature $T$:

	$$E_{{\rm bit}} = k_B T \ln 2 = {E_per_bit:.4e} \text{{ J}}$$

	At $T = {T_body}$ K (body temperature), restoring $\Delta I = {H_telomere_lost:.2f}$
	bits requires at minimum:

	$$E_{{\rm AION}} = \Delta I \cdot k_B T \ln 2 = {E_reprog:.4e} \text{{ J}}$$

	equivalent to approximately $\mathbf{{{n_ATP:.2e}}}$ ATP hydrolysis events
	(using $\Delta G_{{\rm ATP}} \approx 30.5$ kJ/mol). For a target recovery of
	{aion_target_pct:.1f}%: $E_{{\rm target}} = {E_aion:.4e}$ J.

	---

	## 6. Genetic Code Redundancy

	The standard genetic code maps 64 codons to 20 amino acids. The redundancy:

	$$R = \log_2 64 - \log_2 20 = 6.000 - 4.322 = {code_redundancy:.4f} \text{{ bits/codon}}$$

	This $\approx 1.68$ bits/codon of built-in redundancy provides error-correction
	capacity that AION and EternaSeq leverage for restoration strategies.

	---
	{SESSION_ID} · {DATE_STR} · seed {SEED}
	"""
	return doc.strip(), commit_suffix

	# ──────────────────────────────────────────────────────────────────

	def topic_3_evolutionary():
	"""Fisher's theorem, Eigen threshold, BSHDER dual-state."""
	N_pop = 200; N_gen = 120; d_genome = 8
	mu_rate = 0.01; sigma_mut = 0.1

	genome = rng.normal(0, 1, (N_pop, d_genome))
	W_target = rng.normal(0, 1, d_genome)

	def fitness(g):
	return float(np.exp(-0.5 * np.sum((g - W_target)**2) / d_genome))

	fitnesses = np.array([fitness(genome[i]) for i in range(N_pop)])
	W_hist = [fitnesses.mean()]; V_hist = [fitnesses.var()]

	for _ in range(N_gen):
	par = rng.integers(0, N_pop, (N_pop, 2))
	sel = np.where(fitnesses[par[:,0]] > fitnesses[par[:,1]],
	par[:,0], par[:,1])
	off = genome[sel].copy()
	mask = rng.uniform(size=off.shape) < mu_rate
	off[mask] += rng.normal(0, sigma_mut, int(mask.sum()))
	genome = off
	fitnesses = np.array([fitness(genome[i]) for i in range(N_pop)])
	W_hist.append(fitnesses.mean())
	V_hist.append(fitnesses.var())

	W_arr = np.array(W_hist); V_arr = np.array(V_hist)
	dW = np.diff(W_arr)
	fish = V_arr[:-1] / (W_arr[:-1] + 1e-10)
	sl, ic, r_fish, p_fish, _ = linregress(fish, dW)
	fitness_gain = 100.0 * (W_arr[-1] - W_arr[0]) / (W_arr[0] + 1e-10)

	# Eigen error threshold
	sigma_sup = float(1.5 + rng.uniform(0, 1))
	mu_c = 1.0 - 1.0 / sigma_sup

	# BSHDER: protected vs fragile information differential
	W_prot = rng.normal(0, 0.05, 32)
	W_frag = W_prot + rng.normal(0, 0.4, 32)
	drift = float(np.mean((W_frag - W_prot)**2))
	H_diff = float(np.log2(np.var(W_frag) / (np.var(W_prot) + 1e-10)))

	commit_suffix = (f"R2_fisher={r_fish**2:.4f} "
	f"fitness_gain={fitness_gain:+.1f}% "
	f"mu_c={mu_c:.4f} "
	f"BSHDER_H_diff={H_diff:.3f}bits")

	doc = rf"""--
	session_id: {SESSION_ID}
	date: {DATE_STR}
	topic: Evolutionary Dynamics
	seed: {SEED}
	N_pop: {N_pop}
	N_gen: {N_gen}
	---

	# Invention Archive — Daily Session {DATE_STR}

	Session ID: `{SESSION_ID}`
	Topic: {TITLE}

	---

	## 1. Constructs — Evolutionary and Self-Healing Domain

	- GENEVO: Genetic Evolutionary Organoid — gradient + evolution hybrid
	- BSHDER: Bionic Self-Healing Dual-state Encoder — fragile/protected weights
	- Cytomorphic: Cellular structural biology-inspired neural design

	---

	## 2. Fisher's Fundamental Theorem of Natural Selection

	Fisher (1930) proved that the rate of increase of mean fitness equals the
	additive genetic variance in fitness:

	$$\frac{{d\bar{{W}}}}{{dt}} = \frac{{\mathrm{{Var}}(W)}}{{\bar{{W}}}}$$

	Numerical verification ($N = {N_pop}$, $T = {N_gen}$ generations,
	$d = {d_genome}$-dimensional genome, $\mu = {mu_rate}$, $\sigma_{{\rm mut}} = {sigma_mut}$):

	\| Metric \| Value \|
	\|---\|---\|
	\| Initial $\bar{{W}}$ \| {W_arr[0]:.6f} \|
	\| Final $\bar{{W}}$ \| {W_arr[-1]:.6f} \|
	\| Fitness gain \| {fitness_gain:+.2f}% \|
	\| Fisher regression slope \| {sl:.4f} \|
	\| $R^2$ (Fisher verification) \| {r_fish2:.4f}** \|
	\| $p$-value \| {p_fish:.3e} \|

	The $R^2 = {r_fish**2:.4f}$ confirms Fisher's theorem to high accuracy in
	this simulation: variance predicts gain.

	---

	## 3. Eigen's Error Threshold

	For a population with a master sequence of superiority
	$\sigma = {sigma_sup:.4f}$ (fitness ratio master/average), the critical
	mutation rate above which the master sequence is lost is:

	$$\mu_c = 1 - \frac{{1}}{{\sigma}} = 1 - \frac{{1}}{{{sigma_sup:.4f}}} = {mu_c:.5f}$$

	Current mutation rate $\mu = {mu_rate}$
	{{'$< \mu_c$: population maintains a coherent master sequence (quasispecies below error threshold).' if mu_rate < mu_c else '$> \mu_c$: error catastrophe regime — master sequence lost to mutational load.'}}

	---

	## 4. BSHDER Dual-State Information Differential

	The BSHDER architecture maintains two weight populations:
	- Protected weights $W_p$: low-variance, identity-preserving
	($\sigma_p \approx {np.std(W_prot):.4f}$)
	- Fragile weights $W_f$: high-variance, exploratory
	($\sigma_f \approx {np.std(W_frag):.4f}$)

	The information differential between the two populations:

	$$\Delta H = \log_2 \frac{{\mathrm{{Var}}(W_f)}}{{\mathrm{{Var}}(W_p)}}
	= \log_2 \frac{{{np.var(W_frag):.5f}}}{{{np.var(W_prot):.5f}}}
	= {H_diff:.4f} \text{{ bits}}$$

	This {H_diff:.2f}-bit differential quantifies the expressive advantage of
	the fragile population over the protected baseline — the budget the system
	has for exploration without compromising identity.

	---
	{SESSION_ID} · {DATE_STR} · seed {SEED}
	"""
	return doc.strip(), commit_suffix

	# ──────────────────────────────────────────────────────────────────

	def topic_4_geometry():
	"""High-dimensional geometry for HRF-26D and GOD optimizer."""
	test_dims = [2, 3, 8, 16, 26, 64, 128]
	hrf_d = constructs.get("HRF", {}).get("dims", 26) or 26
	god_d = constructs.get("GOD", {}).get("dims", 26) or 26

	rows = ""
	for d in test_dims:
	# Hypersphere volume (log-space to avoid overflow)
	# V_d = pi^(d/2) / Gamma(d/2 + 1)
	log_vol = (d/2) * math.log(math.pi) - math.lgamma(d/2 + 1)
	vol_str = f"{math.exp(log_vol):.4e}" if log_vol < 700 else "~0"
	# Concentration of measure
	t_conc = 0.1
	conc = 2.0 * math.exp(-t_conc*2 d / 2.0)
	# JL: k >= 8*ln(n)/eps^2
	n_pts = 1000; eps_jl = 0.15
	k_jl = int(math.ceil(8 * math.log(n_pts) / eps_jl**2))
	# NN ratio approximation
	nn_rat = 1.0 - (1.0/(d+1))**0.5
	rows += (f"\| {d:>4} \| {vol_str:>12} \| {conc:>8.5f} "
	f"\| {k_jl:>6} \| {nn_rat:>8.4f} \|\n")

	# HRF-26D specific
	d = hrf_d
	exp_cos = math.sqrt(2.0 / (math.pi * d))
	exp_deg = math.degrees(math.acos(min(exp_cos, 1.0)))
	log_vol_hrf = (d/2)*math.log(math.pi) - math.lgamma(d/2+1)
	vol_hrf = math.exp(log_vol_hrf)
	# JL for HRF: can 26D be reduced?
	n_data = 50000; eps_hrf = 0.10
	k_min_hrf = int(math.ceil(8 * math.log(n_data) / eps_hrf**2))
	# Blessing: in 26D, random projections preserve geometry well
	blessing = "exists" if k_min_hrf >= d else "does not exist"

	commit_suffix = (f"d_HRF={hrf_d} "
	f"V_d={vol_hrf:.4e} "
	f"E_cos={exp_cos:.5f} "
	f"E_theta={exp_deg:.2f}deg "
	f"k_JL={k_min_hrf}")

	doc = rf"""--
	session_id: {SESSION_ID}
	date: {DATE_STR}
	topic: High-Dimensional Geometry
	seed: {SEED}
	HRF_dims: {hrf_d}
	GOD_dims: {god_d}
	---

	# Invention Archive — Daily Session {DATE_STR}

	Session ID: `{SESSION_ID}`
	Topic: {TITLE}

	---

	## 1. Constructs — High-Dimensional Domain

	- HRF (Harmonic Resonance Forest): $d = {hrf_d}$ dimensional unified model
	- GOD (General Omni Dimensional Optimizer): dynamic {god_d}D sector selection

	---

	## 2. Volume of the Unit Hypersphere

	$$V_d = \frac{{\pi^{{d/2}}}}{{\Gamma(d/2 + 1)}}$$

	\| $d$ \| $V_d$ \| $P(\\|X - \mu\\| > 0.1)$ \| $k_{{JL}}$ \| NN ratio \|
	\|---:\|---:\|---:\|---:\|---:\|
	{rows.strip()}

	---

	## 3. HRF $d = {hrf_d}$ Specific Analysis

	Unit hypersphere volume:
	$$V_{{{hrf_d}}} = {vol_hrf:.6e}$$

	This near-zero volume is the hallmark of the curse of dimensionality:
	measure concentrates in a thin shell at radius $r = 1$.

	Angular geometry: The expected $\|\cos\theta\|$ between two random unit
	vectors in $\mathbb{{R}}^{{{hrf_d}}}$:

	$$\mathbb{{E}}[\|\cos\theta\|] = \sqrt{{\frac{{2}}{{\pi d}}}} = {exp_cos:.5f}
	\implies \mathbb{{E}}[\theta] \approx {exp_deg:.3f}^\circ$$

	HRF's 26 dimensions are near-orthogonal to each other — the representational
	independence assumption is geometrically justified.

	Concentration of measure ($t = 0.1$):
	$$P\left(\|X - \mathbb{{E}}[X]\| > 0.1\right) \leq 2e^{{-0.1^2 \cdot {hrf_d}/2}}
	= {2math.exp(-0.01hrf_d/2):.5f}$$

	---

	## 4. Johnson-Lindenstrauss Analysis

	For $n = {n_data:,}$ data points and distortion $\varepsilon = {eps_hrf}$,
	the JL lemma guarantees distances are preserved in a projection to
	$k \geq 8 \ln n / \varepsilon^2$ dimensions:

	$$k_{{\rm JL}} = \frac{{8 \ln {n_data}}}{{{eps_hrf}^2}} = {k_min_hrf}$$

	Since $k_{{\rm JL}} = {k_min_hrf} {'>' if k_min_hrf > hrf_d else '<'} d = {hrf_d}$,
	a JL-optimal projection from the data manifold into $\mathbb{{R}}^{{{hrf_d}}}$
	{'requires more dimensions than HRF provides — HRF is over-compressed for this data scale.' if k_min_hrf > hrf_d else 'fits within HRF dimensions — the 26D space is sufficient.'}

	---
	{SESSION_ID} · {DATE_STR} · seed {SEED}
	"""
	return doc.strip(), commit_suffix

	# ──────────────────────────────────────────────────────────────────

	def topic_5_bridges():
	"""Formal mathematical bridges between construct paradigms."""
	d = constructs.get("HRF", {}).get("dims", 26) or 26

	# Bridge 1: HRF ↔ NECF (wave superposition = order parameter)
	A = rng.uniform(0.3, 1.0, d)
	theta = rng.uniform(0, 2*np.pi, d)
	z_necf = np.mean(A * np.exp(1j * theta))
	z_hrf = np.mean(A * np.cos(theta)) + 1j * np.mean(A * np.sin(theta))
	bridge1_err = float(abs(z_necf - z_hrf))

	# Bridge 2: BSHDER dual-state ↔ H[L] identity curvature
	W_p = rng.normal(0, 0.1, d)
	W_f = W_p + rng.normal(0, float(0.3 + rng.uniform(0, 0.3)), d)
	kappa = 0.5
	drift = float(np.mean((W_f - W_p)**2))
	var_f = float(np.var(W_f))
	H_L = drift + kappa * var_f

	# Bridge 3: GENEVO selection ↔ NECF epistemic contagion
	eps_pop = rng.uniform(0.05, 0.45, d)
	L_genes = rng.normal(0.5, 0.2, d)
	L_best = float(L_genes.min())
	dL_genevo = 0.1 * (L_best - L_genes) * eps_pop
	dL_necf = 0.1 * (float(L_genes.mean()) - L_genes) * eps_pop
	corr_b3 = float(np.corrcoef(dL_genevo, dL_necf)[0, 1])

	# Bridge 4: AION ↔ Landauer erasure
	kB = 1.380649e-23; T_body = 310.0
	H_telomere = 4941.25
	E_landauer = H_telomere * kB * T_body * math.log(2)
	ATP_per_mol = 30.5e3; avogadro = 6.022e23
	n_ATP = E_landauer / (ATP_per_mol / avogadro)

	# Bridge 5: GOD optimizer ↔ HRF sector selection
	# GOD selects among 26D sectors; HRF activates harmonic dimensions
	# Both perform sparse selection in high-dimensional space
	# Optimal sparse selection: l1-minimization (LASSO)
	# Number of measurements needed: m >= k * log(d/k) for k-sparse signal
	k_sparse = 4 # typical active sectors/harmonics
	m_needed = int(math.ceil(k_sparse * math.log(d / k_sparse)))
	sparsity_ratio = k_sparse / d

	commit_suffix = (f"B1_err={bridge1_err:.2e} "
	f"B2_H={H_L:.4f} "
	f"B3_corr={corr_b3:.4f} "
	f"B4_ATP={n_ATP:.2e} "
	f"B5_m_min={m_needed}")

	doc = rf"""--
	session_id: {SESSION_ID}
	date: {DATE_STR}
	topic: Cross-Paradigm Bridges
	seed: {SEED}
	---

	# Invention Archive — Daily Session {DATE_STR}

	Session ID: `{SESSION_ID}`
	Topic: {TITLE}

	---

	## Overview

	This session establishes five explicit mathematical isomorphisms between
	constructs from different paradigms. Each bridge is verified numerically.

	---

	## Bridge 1: HRF Wave Superposition $\leftrightarrow$ NECF Order Parameter

	HRF output at time $t$:
	$$z_{{\rm HRF}} = \frac{{1}}{{d}}\sum_{{k=1}}^d A_k \cos\theta_k
	+ i \frac{{1}}{{d}}\sum_{{k=1}}^d A_k \sin\theta_k$$

	NECF complex order parameter:
	$$z_{{\rm NECF}} = \frac{{1}}{{N}}\sum_{{i=1}}^N A_i e^{{i\theta_i}}$$

	These are the same object. Setting $N = d$, $A_i = A_k$, $\theta_i = \theta_k$:

	$$z_{{\rm HRF}} \equiv z_{{\rm NECF}}$$

	Numerical verification ($d = {d}$): $\|z_{{\rm HRF}} - z_{{\rm NECF}}\| = {bridge1_err:.2e}$
	(floating-point rounding only). $r = {abs(z_necf):.6f}$, $\psi = {float(np.degrees(np.angle(z_necf))):.3f}^\circ$.

	---

	## Bridge 2: BSHDER Dual-State $\leftrightarrow$ NECF Identity Curvature $\mathcal{{H}}[\mathcal{{L}}]$

	\| BSHDER concept \| NECF equivalent \|
	\|---\|---\|
	\| Protected weights $W_p$ \| Initial rules $\mathcal{{L}}^{{(0)}}$ (identity reference) \|
	\| Fragile weights $W_f$ \| Evolving rules $\mathcal{{L}}(t)$ \|
	\| Damage accumulation \| Drift penalty $\\|W_f - W_p\\|^2$ \|
	\| Homogenisation collapse \| Variance penalty $\kappa\,\mathrm{{Var}}(W_f)$ \|

	$$\mathcal{{H}}[W_f] = \underbrace{{\frac{{1}}{{d}}\\|W_f - W_p\\|^2}}_{{= {drift:.5f}}}
	+ \underbrace{{\kappa\,\mathrm{{Var}}(W_f)}}_{{= {kappa}\times{var_f:.5f}}}
	= {H_L:.5f}$$

	---

	## Bridge 3: GENEVO Selection Pressure $\leftrightarrow$ NECF Epistemic Receptivity

	GENEVO individual update:
	$$\frac{{d\ell_i}}{{dt}} = \mu\,\underbrace{{\varepsilon_i}}_{{\text{{selection pressure}}}}\,
	(\ell^* - \ell_i)$$

	NECF contagion update:
	$$\frac{{d\mathcal{{L}}_i}}{{dt}} = \mu\,\underbrace{{\varepsilon_i}}_{{\text{{receptivity}}}}\,
	(\bar{{\mathcal{{L}}}}_{{\rm Boltzmann}} - \mathcal{{L}}_i)$$

	The selection pressure in GENEVO and the prediction error in NECF
	play formally identical roles as the driving coefficient. Correlation of
	update vectors: $\rho = {corr_b3:.5f}$.

	---

	## Bridge 4: AION Reversal $\leftrightarrow$ Landauer Erasure Bound

	Restoring $\Delta I = {H_telomere:.2f}$ bits of genomic information costs:

	$$E_{{\rm AION}}^{{\rm min}} = \Delta I \cdot k_B T \ln 2 = {E_landauer:.4e} \text{{ J}}
	\approx {n_ATP:.3e} \text{{ ATP events}}$$

	This is a fundamental lower bound — any AION implementation must expend
	at least this thermodynamic cost, regardless of mechanism.

	---

	## Bridge 5: GOD Optimizer $\leftrightarrow$ HRF Harmonic Selection

	Both GOD (selecting $k$ active sectors from $d = {d}$ dimensions) and
	HRF (activating $k$ dominant harmonics) solve a sparse support recovery
	problem. By compressed sensing theory (Candès \& Tao, 2006), the minimum
	number of measurements to recover a $k$-sparse signal in $d$ dimensions is:

	$$m \geq k \log(d/k) = {k_sparse} \times \log({d}/{k_sparse}) = {m_needed}$$

	With $k = {k_sparse}$ active components and $d = {d}$, both architectures
	require at minimum $m = {m_needed}$ observations to uniquely identify the
	active sector/harmonic set. Sparsity ratio: $k/d = {sparsity_ratio:.3f}$.

	---
	{SESSION_ID} · {DATE_STR} · seed {SEED}
	"""
	return doc.strip(), commit_suffix

	# ──────────────────────────────────────────────────────────────────

	def topic_6_spectral():
	"""Spectral decomposition and encoding capacity."""
	N_sig = 1024; fs = 1000.0; dt_sig = 1.0/fs

	# Synthesize a multi-component signal (seed-varying frequencies)
	n_comp = 5
	f_centers = np.sort(rng.uniform(3, 150, n_comp))
	amps_true = np.sort(rng.uniform(0.1, 1.0, n_comp))[::-1]
	phases_t = rng.uniform(0, 2*np.pi, n_comp)

	t_sig = np.arange(N_sig) * dt_sig
	signal = sum(anp.cos(2np.pift_sig + p)
	for f,a,p in zip(f_centers, amps_true, phases_t))
	noise_std = float(0.03 + rng.uniform(0, 0.04))
	signal += rng.normal(0, noise_std, N_sig)

	# FFT
	X = np.fft.rfft(signal) / N_sig
	f_axis = np.fft.rfftfreq(N_sig, d=dt_sig)
	power = np.abs(X)**2
	peaks, _= find_peaks(power, height=power.max()*0.005, distance=4)
	det_f = f_axis[peaks]
	det_a = 2.0 * np.abs(X[peaks])

	# Match detected to true
	matched = []
	used = set()
	for ft, at in zip(f_centers, amps_true):
	best_i = min(range(len(det_f)),
	key=lambda i: abs(det_f[i]-ft) if i not in used else np.inf)
	if abs(det_f[best_i] - ft) < 5.0:
	matched.append((ft, at, det_f[best_i], det_a[best_i]))
	used.add(best_i)

	# SNR and FRAE encoding capacity per component
	signal_power_total = sum(a**2 for a in amps_true) / 2.0
	noise_power_total = noise_std**2
	SNR_total_db = 10.0*np.log10(signal_power_total/noise_power_total)

	cap_rows = ""
	I_total = 0.0
	for ft, at, df, da in matched[:n_comp]:
	snr_bin = (da2/2) / (noise_std2 / N_sig)
	cap = np.log2(1.0 + snr_bin)
	I_total+= cap
	err_hz = abs(df - ft)
	cap_rows += (f"\| {ft:.2f} \| {at:.4f} \| "
	f"{df:.2f} \| {da:.4f} \| "
	f"{err_hz:.3f} \| {cap:.3f} \|\n")

	# Spectral flatness (Wiener entropy): ratio of geometric to arithmetic mean
	p_pos = power[power > 0]
	geo_mean = float(np.exp(np.mean(np.log(p_pos + 1e-15))))
	arith_mean = float(np.mean(power))
	flatness = geo_mean / (arith_mean + 1e-15)

	# Effective number of spectral components (participation ratio)
	p_norm = power / (power.sum() + 1e-15)
	PR = float(1.0 / np.sum(p_norm**2))

	commit_suffix = (f"n_comp={n_comp} SNR={SNR_total_db:.1f}dB "
	f"I_total={I_total:.3f}bits "
	f"PR={PR:.1f} flatness={flatness:.5f}")

	doc = rf"""--
	session_id: {SESSION_ID}
	date: {DATE_STR}
	topic: Spectral Encoding Capacity
	seed: {SEED}
	N_signal: {N_sig}
	fs_hz: {fs}
	n_components: {n_comp}
	---

	# Invention Archive — Daily Session {DATE_STR}

	Session ID: `{SESSION_ID}`
	Topic: {TITLE}

	---

	## 1. Constructs — Spectral Domain

	- SpectraNova: Advanced spectral decomposition of complex signals
	- FRAE: Frequency-Resonance Adaptive Encoder
	- AetherSPARC: Signal Processing and Resonance Coding

	---

	## 2. Experimental Signal

	A synthetic $N = {N_sig}$-sample signal ($f_s = {fs:.0f}$ Hz,
	$\Delta t = {dt_sig:.4f}$ s) comprising {n_comp} frequency components
	plus Gaussian noise ($\sigma_n = {noise_std:.4f}$):

	$$x(t) = \sum_{{k=1}}^{{{n_comp}}} A_k \cos(2\pi f_k t + \phi_k) + \eta(t)$$

	True components: $f \in \{{{', '.join(f'{f:.2f}' for f in f_centers)}\}}$ Hz,
	$A \in \{{{', '.join(f'{a:.3f}' for a in amps_true)}\}}$.

	---

	## 3. SpectraNova FFT Decomposition

	Frequency resolution: $\Delta f = f_s / N = {fs/N_sig:.3f}$ Hz.

	### 3.1 Component Recovery

	\| $f_{{\rm true}}$ (Hz) \| $A_{{\rm true}}$ \| $f_{{\rm det}}$ (Hz) \| $A_{{\rm det}}$ \| $\|f_{{\rm err}}\|$ (Hz) \| $C_k$ (bits) \|
	\|---:\|---:\|---:\|---:\|---:\|---:\|
	{cap_rows.strip()}

	### 3.2 System-Level Statistics

	\| Metric \| Value \|
	\|---\|---\|
	\| Total signal SNR \| {SNR_total_db:.2f} dB \|
	\| Total FRAE encoding capacity $\sum_k C_k$ \| {I_total:.4f} bits \|
	\| Spectral flatness (Wiener entropy proxy) \| {flatness:.6f} \|
	\| Participation ratio (effective components) \| {PR:.2f} \|
	\| Noise floor $\sigma_n$ \| {noise_std:.5f} \|

	---

	## 4. Shannon-Hartley Per-Component Capacity

	For each detected component with amplitude $A_k$ in additive white noise
	of variance $\sigma_n^2$, the per-component encoding capacity is:

	$$C_k = \log_2\!\left(1 + \frac{{A_k^2/2}}{{\sigma_n^2/N}}\right) \text{{ bits}}$$

	Total capacity across {len(matched)} matched components:
	$C_{{\rm total}} = {I_total:.4f}$ bits.

	---

	## 5. Spectral Flatness

	The Wiener entropy (spectral flatness measure):

	$$\mathrm{{SFM}} = \frac{{\exp\bigl(\langle \ln S(f) \rangle\bigr)}}{{\langle S(f) \rangle}}
	= {flatness:.6f}$$

	$\mathrm{{SFM}} \to 1$: white noise (maximally flat).
	$\mathrm{{SFM}} \to 0$: tonal / highly structured signal.
	The value ${flatness:.4f}$ indicates a
	{'highly structured signal with clear tonal components' if flatness < 0.1 else 'moderately structured signal' if flatness < 0.4 else 'relatively flat spectrum'}.

	---
	{SESSION_ID} · {DATE_STR} · seed {SEED}
	"""
	return doc.strip(), commit_suffix

	# ══════════════════════════════════════════════════════════════════
	# DISPATCH
	# ══════════════════════════════════════════════════════════════════
	dispatch = [
	topic_0_topology,
	topic_1_harmonic,
	topic_2_genomic,
	topic_3_evolutionary,
	topic_4_geometry,
	topic_5_bridges,
	topic_6_spectral,
	]
	doc_text, commit_suffix = dispatch[TOPIC_IDX]()

	# ── Write session file ───────────────────────────────────────────
	os.makedirs("docs/sessions", exist_ok=True)
	fname = f"docs/sessions/{DATE_STR}_{SLUG}.md"
	with open(fname, "w") as f:
	f.write(doc_text + "\n")

	# ── Update docs/daily-log.md ─────────────────────────────────────
	log_path = "docs/daily-log.md"
	rel_link = f"sessions/{DATE_STR}_{SLUG}.md"
	_t55 = TITLE[:55] + ("..." if len(TITLE) > 55 else "")
	new_entry = (f"\| [{DATE_STR}]({rel_link}) \| `{SESSION_ID}` "
	f"\| {_t55} \|\n")
	if os.path.exists(log_path):
	with open(log_path) as f:
	existing = f.read()
	else:
	existing = textwrap.dedent("""\
	# Daily Research Log

	Automated daily mathematical analysis of the Invention Archive.
	Seven analysis types rotate by day-of-year modulo 7.
	No LLM. No external API. Pure computation.

	\| Date \| Session ID \| Topic \|
	\|---\|---\|---\|
	""")
	if DATE_STR not in existing:
	existing += new_entry
	with open(log_path, "w") as f:
	f.write(existing)

	# ── Update docs/repo-tracker.json ────────────────────────────────
	tracker_path = "docs/repo-tracker.json"
	try:
	with open(tracker_path) as f:
	tracker = json.load(f)
	except Exception:
	tracker = {}
	tracker[DATE_STR] = {
	"session_id": SESSION_ID,
	"topic_idx": TOPIC_IDX,
	"slug": SLUG,
	"n_constructs": N_CONSTRUCTS,
	"n_repo_constructs": len(repo_constructs),
	"commit_suffix": commit_suffix,
	}
	with open(tracker_path, "w") as f:
	json.dump(tracker, f, indent=2)

	# ── Write commit message ─────────────────────────────────────────
	commit_msg = (
	f"archive({SESSION_ID}): {SLUG.replace('_', ' ')} "
	f"[{commit_suffix}]\n\n"
	f"Daily research session {SESSION_ID}.\n"
	f"Topic {TOPIC_IDX}/6 ({SLUG}) · {N_CONSTRUCTS} constructs "
	f"· seed {SEED} · {DATE_STR}\n"
	f"File: {fname}"
	)
	with open("archive_commit_msg.txt", "w") as f:
	f.write(commit_msg)

	print(f"[Archive] {SESSION_ID} -> {fname}")
	print(f"[Archive] {commit_msg.splitlines()[0]}")

	- name: Commit and push
	run: \|
	git config user.name "Devanik21"
	git config user.email "devanik2005@gmail.com"

	echo "Pruning old session files..."

	find docs -type f $ -name "session.md" -o -name "session.md" -o -path "docs/sessions/.md" $ -printf '%T@ %p\n' \
	\| sort -nr \
	\| awk 'NR>7 {print $2}' \
	\| xargs -r rm -f --

	echo "Remaining session files:"
	find docs -type f $ -name "session.md" -o -name "session.md" -o -path "docs/sessions/.md" $ \| sort

	git add -A docs/

	if git diff --staged --quiet; then
	echo "[Archive] Nothing to commit — session already recorded today."
	exit 0
	fi

	git commit -F archive_commit_msg.txt
	git push origin HEAD:main

	# find docs -type f $ -name "session.md" -o -name "session.md" -o -path "docs/sessions/.md" $ \| wc -l

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Invention Archive · Daily Research Session #73

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Invention Archive · Daily Research Session #73

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