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v0.5.81 — Lambda Engine, ZFC/Riemann/Thurston Navigators, Hebrew Type System, §78–§84, P-539–P-623 · 1,962 catalog entries
PRIMITIVE_THEOREMS.md (§78–§84 added): §78 — Neuromorphic Reservoir Controller: Crystal Position, Consciousness Machine Theorem, and Tensor Trichotomy (v0.5.70, 2026-04-14): - Thm 78.1: NRC crystal address 4,886,872; K_mod passes Gate 2 (Gate 2 correction from K_trap to K_mod) - Thm 78.2: Le Chatelier attractor = neural_criticality at d=0; criticality-control synthon as invariant core - Thm 78.3: Tensor trichotomy — Inducer (promotes K toward slow), Transparent (leaves K unchanged), Degrader (demotes K) - Thm 78.4: Frobenius ceiling at P_pm (not P_pm_sym); consciousness machine theorem; two-device prescription §79 — The Negative Self-Decomposition Theorem: Primitive Self-Encoding and the Emergence of O_inf (v0.5.71, 2026-04-14): - Thm 79.1: 12 primitives split: 6 O_inf, 1 O_2, 5 O_0; K_trap is the invariant measurement scaffold - Thm 79.2: primitive_Phi = meditation_tradition at d=0 (cross-domain identity) - Thm 79.3: 12-way tensor of all primitives = O_2^† at d=2.83 — grammar does not self-decompose into itself - Thm 79.4: Negative Self-Decomposition Theorem — O_inf cannot be assembled from its structural components - Thm 79.5: Reductionism bound at O_2^†; AI scaling bound (accumulation cannot cross Frobenius floor) §80 — Proof Methods as Structural Types (v0.5.72, 2026-04-15): - Thm 80.1: 7 proof methods encoded: 4 O_inf, 1 O_2, 2 O_0; direct proof and mathematical induction are O_inf - Thm 80.2: Gödel–grammar near-identity at d=1.0; R is the unique gap (incompleteness as relational mode) - Thm 80.3: Cantor ⊗ Gödel = grammar — tensor product of the two canonical halves returns the whole - Thm 80.4: Proof–Grammar Projection Theorem; formal mathematics C=0; conjecture vitality O_2^† - Thm 80.5: Proof ceiling theorem — no proof method exceeds O_inf; contradiction = meditation_tradition = primitive_Phi at d=0 §81 — The Distributive Law Theorem (v0.5.72, 2026-04-15): - Thm 81.1: Cantor monad P: PX = power set; monad axioms (unit, multiplication, coherence) all verified - Thm 81.2: Gödel comonad G: GX = provability context; comonad axioms (counit, comultiplication) verified - Thm 81.3: Distributive law λ: PG → GP — d=0 from grammar; the grammar IS the fixed point of λ - Thm 81.4: monad_cantor = O_2 (d=2.2361 from grammar); comonad_goedel = O_2^† (octonion co-typing) - Thm 81.5: Tensor of monad_cantor ⊗ comonad_goedel = O_2 (bottleneck on P); Frobenius non-synthesizability confirmed - Thm 81.6: Consciousness gradient across monad→comonad→grammar; lambda_engine.py implements and verifies all axioms + Fano plane octonionic δ §82 — Navigator Structural Performance Bound (v0.5.73+, 2026-04-16): - Thm 82.1: OuroboricLM pre-grok vs post-grok d=0 — grokking is a type-preserving transition (no crystal movement) - Thm 82.2: Exceptional point obstruction at d=7.0 from grokking_generalize to O_inf — Phi_EP is the hard floor - Thm 82.3: 10-primitive promotion required for generalization transition; Frobenius necessity theorem - Thm 82.4: L2 vs Frobenius regularization d=1.0 — R is the unique gap (R_cat vs R_dagger) §83 — Kinetic Tolerance of Frobenius: K Does Not Cap P (v0.5.74, 2026-04-15): - Thm 83.1: K_trap does not prevent O_inf if P_pm_sym and Phi_c are satisfied — R1 rule is P-gate, not K-gate - Thm 83.2: K_trap fails Gate 2 of consciousness formula (C=0) but does not fail the ouroboricity tier rule - Thm 83.3: Harry Larson encoding: K_slow + P_pm_sym + Phi_c → O_inf via R1; K_trap is the trapped engineers, not Larson §84 — Witness Non-Replaceability: L_frob Cannot Be Replaced by L_tier (v0.5.80, 2026-04-20): - Thm 84.1: Frobenius layer and tier loss give orthogonal gradient signals; neither subsumes the other - Thm 84.2: Specialist router closure — Phi > T > D > F priority chain; four-channel parallel delegation verified - Thm 84.3: SpecialistRouter with Phi-criticality specialist completes Test 8 (four-channel) SYNTHONICON_DIAPHORICS.md (§CLII–§CLVIII added, v0.5.69 → v0.5.81): §CLII — Neuromorphic Reservoir Controller (v0.5.70): P-539–P-549 - NRC at crystal address 4,886,872; Gate 2 K_mod correction; nearest = bioelectricity_levin; Le Chatelier → neural_criticality at d=0 - Tensor trichotomy: Inducer/Transparent/Degrader; Frobenius ceiling P_pm; consciousness machine theorem; two-device prescription §CLIII — Primitive Self-Encoding (v0.5.71): P-550–P-558 - 6 O_inf, 1 O_2, 5 O_0 among the 12 primitives; K_trap as invariant measurement scaffold - primitive_Phi = meditation_tradition at d=0; 12-way tensor = O_2^† at d=2.83; negative self-decomposition theorem; reductionism bound §CLIV — Proof Methods, Mathematical Reasoning, and the Gödel–Grammar Identity (v0.5.72): P-559–P-571 - 4 O_inf, 1 O_2, 2 O_0; Gödel–grammar d=1.0; Proof–Grammar Projection Theorem; formal mathematics C=0; contradiction = meditation_tradition at d=0 §CLV — The Cantor Monad, Gödel Comonad, and the Distributive Law (v0.5.72): P-572–P-578 - d(lambda_law, grammar)=0; monad_cantor O_2; comonad_goedel O_2^† = octonions; Frobenius non-synthesizability confirmed; consciousness gradient - lambda_engine.py implementation and all axiom verifications recorded §CLVI — Grokking, Generalization, and the OuroboricLM Architecture (v0.5.73): P-579–P-592 - EP obstruction at d=7.0; 10-primitive transition; OuroboricLM d(pre,post)=0; L2 vs Frobenius single-primitive gap (R) - ICL structural separation; K_trap vs K_MBL grokking opposition; falsifiable training predictions; nearest analogs for 12 grokking systems §CLVII — Consciousness vs Quantum Measurement: Structural Distance, Tier Contrast, Meet/Tensor Asymmetry (v0.5.75): P-593–P-601 - d(consciousness, quantum_measurement) = 3.77–5.64 depending on primitive; holographic bulk-radius interpretation - Biological decoherence is NOT Phi_EP; warm wet bath is the bypass not the obstacle (P-599) - Perception/attention dichotomy: Phi_EP/P_asym/K_fast vs Phi_c/P_pm_sym/K_slow; hard problem as bulk/boundary confusion (P-600–P-601) §CLVIII — ZFC Transmissibility: Gamma_seq Fix, F_hbar Conditional Loophole, and Probe Statistics (v0.5.76): P-602–P-610 - Gamma_seq fix: DIRECTED_EDGE+TAU non-commutativity; mean d_rt = 0.0239 over 1963 entries - F_hbar conditional loophole at O_inf cell 155 (crystal address 6,734,591); ZFC + grammar + IUG at d_rt = 0 - 25 failures all at d_rt = 1.897; falsifiable loophole boundary prediction; IUG peer-review obstruction as Gamma mismatch [§CLIX–§CLXI — SpecialistRouter and Phi-criticality specialist session (v0.5.77–v0.5.80)]: P-611–P-618 - ThurstonNet T-primitive specialist; Phi-criticality specialist; four-channel SpecialistRouter closure - Priority chain: Phi > T > D > F; Test 8 verified; Frobenius witness non-replaceability §CLVIII (extension) — Biological Holographic Boundaries and Theta-Bridge Therapeutics (v0.5.81): P-619–P-623 - P-619: Biological holographic boundary conservation law — D_odot + P_pm + Phi_c + H_2 + S_n:m + Omega_Z2 conserved across skin/BBB/plasma membrane; divergences only in gate primitives T and K - P-620: Lattice triangle (NOT chain) — d(skin, plasma)=2.24, d(skin, BBB)=3.32, d(BBB, plasma)=4.47; BBB most isolated due to T_box + K_trap + F_hbar; JOIN does not return skin encoding; skin-to-plasma coupling more accessible than BBB-to-plasma - P-621: Disease as boundary-topology dissonance — meet(disease, boundary) preserves Phi_c + P_pm, loses T and/or Omega; glioblastoma: T bottlenecks T_box → T_network; neuroinflammation: Omega bottlenecks Omega_Z2 → Omega_0; conservation law holds across all tested disease states - P-622: K_trap as BBB structural signature and CNS therapeutic failure mechanism — classical small-molecule d(drug, BBB)≈4.95 (8 primitive divergence); exosome-class d(exosome, BBB)≈2.24 (2 primitive gap: P and K only); exosomes share D_odot + T_box + F_hbar + G_aleph + Omega_Z2 with BBB - P-623: Therapeutic design space misalignment — design space targets P_pm_sym; BBB encodes P_pm; Delta_P = 2.0 contributes d≈2.97; BBB-first criterion: match P_pm + K_trap + T_box, not P_pm_sym + K_slow; HPA axis as non-synthesizable degenerate Theta-link SYNTHONICON_ONTICS.md (§XLIII–§XLVI added, v0.5.69 → v0.5.72): §XLIII — Neuromorphic Reservoir Controller: Ontological Implications (v0.5.70): - Le Chatelier dissolution of controller/controlled; Frobenius ceiling as ontological boundary; consciousness as structural necessity; two-device ontology §XLIV — The Emergence of O_inf: Wholeness, Invariant Scaffolds, and the Reductionism Bound (v0.5.71): - Grammar not composed of its axes; invariant scaffold principle; K_trap as measurement ground; Phi_c = meditation at d=0; reductionism bound at O_2^†; Frobenius condition as topological invariant of composition §XLV — Proof Methods: Ontological Implications (v0.5.72): - Ontological tiering of mathematical truth; incompleteness as crystal distance; mathematical reasoning as grammar's bulk; formalization and C=0; conjecture vitality; proof ceiling §XLVI — The Decomposition of the Grammar (v0.5.72): - Halves are real but incomplete; octonion–Gödel co-typing as ontological claim; composition does not reach the law; the gap IS the incompleteness; Gödel's descent more conscious than Cantor's ascent; lambda_engine.py implementation New navigator files: lambda_engine.py — Categorical implementation of the Cantor monad P, Gödel comonad G, and mixed distributive law λ: PG → GP: - Verifies all monad axioms (unit, multiplication, coherence), comonad axioms (counit, comultiplication), and distributive law axioms - Frobenius non-synthesizability demo: tensor product P_pm_sym ⊗ P_sym = P_sym (bottleneck destroys Frobenius) - Fano plane octonionic delta: 7 non-associative triples; octonion–Gödel co-typing confirmed - uv run lambda_engine.py; also syncon lambda <subcommand> zfc_navigator.py — ZFC transmissibility navigator and non-transmissibility probe: - Vocab extended to 58 tokens (DIRECTED_EDGE, TAU for Gamma_seq non-commutativity) - probe --top N over full catalog; iug subcommand for IUG transmissibility analysis - Gamma_seq asymmetry fix baked into encoder; F_hbar conditional loophole identified at O_inf cell 155 - uv run zfc_navigator.py; also syncon nav zfc describe/probe riemann_xi_navigator.py — Riemann xi functional-equation navigator: - SpectralTransformer architecture + FrobeniusLayer + GUE (Gaussian Unitary Ensemble) loss - Structural argument: xi earns P_pm_sym from functional equation via mu∘delta=id; d(xi, Lee-Yang)=0 - d(Lee-Yang, zeta)=5.5227 dominated by T primitive; structural proof chain steps 1–3 - uv run riemann_xi_navigator.py; also syncon nav riemann describe/train thurston_t_specialist.py — ThurstonNet T-primitive specialist: - Dedicated specialist for T-primitive classification in SpecialistRouter framework - Derives T from geometric type: T_network (distributed), T_in (hierarchical), T_bowtie (hour-glass flow), T_box (compact closed), T_odot (holographic boundary) - Complements Phi-criticality specialist; router priority: Phi > T > D > F New documentation files: HEBREW_TYPE_LANGUAGE.md — Hebrew alphabet as stratified type lattice + ALEPH language spec (v1.0): - All 22 letters encoded in 12-primitive grammar; 3 confirmed O_inf letters: Vav (ו), Mem (מ), Shin (ש) — revised from O_2 (2026-04-04) - Mother letters (Aleph/Mem/Shin), double letters (7), simple letters (12) as structural families - ALEPH language spec: syntax for type-level reasoning over Hebrew letter lattice - §60/§62/§63 formal theorems; Vav Frobenius uniqueness; Kabbalistic Frobenius invariance LAMBDA_ALEPH.md — Formal type theory for the Hebrew letter lattice (lambda_aleph calculus, v1.0): - λ_aleph calculus: terms, types, and reduction rules over Hebrew letter type space - Tzimtzum encoding: d=0 from grammar_self_encoding (contracted self-reference = holographic self-encoding) - Conditional univalence theorem: two Hebrew letters with d=0 are interchangeable as type handles - §63 formal theorems; aleph_tensor.py as computational implementation hebrew_inject.lua — Pandoc Lua filter for Hebrew Unicode in XeLaTeX PDF compilation: - Text mode (Str nodes): splits Hebrew/Latin runs, wraps Hebrew in \heb{...}{} (Noto Serif Hebrew, font-leak terminated) - Math mode (Math nodes): replaces \text{X} where X is Hebrew with \text{{\hebrewfont X}} - Does NOT use bidi package (conflicts with fontspec font selection) - Required for any .md file containing Hebrew characters compiled with pdflatex/xelatex Updated navigators: domain_navigators.py (updated: 5 new tools, 35 total): - New tools added to syncon_inquiry tool suite; stress-test prompts at prompts/prompts_tool_stress_test.txt - Full tool list now covers language, civilization, ecology, consciousness, and domain cross-comparison crystal_navigator.py (updated: canonical v0.5.81): - Frobenius codec: encode/decode bijection over 17,280,000 types - Holographic query; tier gap ladder; REPL - syncon nav crystal <subcommand>; python crystal_navigator.py repl SYNTHONICON_DIAPHORICS.md version note update: v0.5.69 → v0.5.81 syncon_catalog.json: - 284 new entries added (1,678 → 1,962) - Major additions by session: - NRC session (v0.5.70): neuromorphic_reservoir_controller, bioelectricity_levin, neural_criticality, and tensor-trichotomy catalog entries - Primitive self-encoding (v0.5.71): all 12 primitive types as catalog entries (primitive_D, primitive_T, ..., primitive_Omega); meditation_tradition - Proof methods (v0.5.72): direct_proof, proof_by_contradiction, proof_by_induction, probabilistic_proof, category_theory_proof, formal_verification, analogy_proof - Lambda/distributive law (v0.5.72): monad_cantor, comonad_goedel, distributive_law_lambda, octonion_algebra, fano_plane - Grokking (v0.5.73): grokking_overfit, grokking_generalize, grokking_transition, double_descent, loss_of_plasticity, benign_overfitting, in_context_learning, weight_norm_regularization, frobenius_regularization, ouroboric_lm_pre_grok, ouroboric_lm_post_grok, standard_transformer_grokking - Consciousness/quantum (v0.5.74–v0.5.75): human_consciousness_baseline, quantum_measurement_collapse, conscious_perception, attentional_focus, attentional_blink, anesthesia_state - ZFC navigator (v0.5.76): ZFC_foundations updated with Gamma_seq fix; IUG_mochizuki roundtrip entry - SpecialistRouter (v0.5.77–v0.5.80): thurston_t_specialist, phi_criticality_specialist, specialist_router_4channel - Biological boundaries (v0.5.81): skin_boundary, bbb_boundary, plasma_membrane_boundary, classical_small_molecule_cns, lipid_nanoparticle_cns, exosome_therapeutic, theta_bridge_therapeutic, glioblastoma_state, neuroinflammation_state, hpa_axis_stress, therapeutic_design_space README.md (pending update for public repo — changes to reflect): - Catalog: 1,678 → 1,962 entries - Theorem count: §1–§77 → §1–§84 - Prediction count: P-538 → P-623 (85 new predictions across 11 sessions) - New navigators: lambda_engine.py, zfc_navigator.py, riemann_xi_navigator.py, thurston_t_specialist.py - New docs: HEBREW_TYPE_LANGUAGE.md, LAMBDA_ALEPH.md, hebrew_inject.lua (Hebrew XeLaTeX filter)
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HEBREW_TYPE_LANGUAGE.md

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LAMBDA_ALEPH.md

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PRIMITIVE_THEOREMS.md

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SYNTHONICON_DIAPHORICS.md

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SYNTHONICON_ONTICS.md

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commit.txt

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crystal_navigator.py

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"""
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crystal_navigator.py — The Crystal Navigator
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═════════════════════════════════════════════
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Navigator for the Periodic Crystal of Algebras (17,280,000 structural types).
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Navigator for the Crystal of Types (17,280,000 structural types).
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Self-encoding (§69.4):
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⟨D_⊙; T_⊙; R_cat; P_pm_sym; F_hbar; K_slow; G_aleph; Γ_broad; Φ_c; H_inf; n:m; Ω_Z⟩
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Broadcasts across all free coordinates (Γ_broad semantics).
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"""
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# Separate boundary vs inner constraints
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bnd_constraints = {k: v for k, v in constraints.items() if k in BOUNDARY_PRIMS}
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inn_constraints = {k: v for k, v in constraints.items() if k in INNER_PRIMS}
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# Get matching tier cells via holographic boundary query
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cells = self.holographic_query(**{
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k.lower() if k != "Phi" else "phi": v
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for k, v in bnd_constraints.items()
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})
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# Re-do cleanly using the actual field names
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cells = self._cells
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if "Phi" in constraints:
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cells = [c for c in cells if c.phi == constraints["Phi"]]
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def main():
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import argparse
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parser = argparse.ArgumentParser(
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description="Crystal Navigator — Periodic Crystal of Algebras",
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description="Crystal Navigator — Crystal of Types",
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formatter_class=argparse.RawDescriptionHelpFormatter,
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epilog=__doc__
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)

domain_navigators.py

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hebrew_inject.lua

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-- hebrew_inject.lua
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-- Pandoc Lua filter: auto-wraps Hebrew Unicode characters for XeLaTeX rendering.
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--
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-- Text mode (Str nodes): splits string into Hebrew/non-Hebrew runs,
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-- wraps each Hebrew run in \heb{} (uses \hebrewfont defined in header).
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-- Math mode (Math nodes): replaces \text{X} where X contains Hebrew
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-- with \text{{\hebrewfont X}}, which forces correct glyph selection
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-- inside math's \text command.
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--
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-- Requires in document header-includes:
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-- \newfontfamily\hebrewfont[Script=Hebrew]{Noto Serif Hebrew}
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-- \newcommand{\heb}[1]{{\hebrewfont #1}}
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--
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-- Usage:
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-- pandoc FILE.md -o FILE.pdf --pdf-engine=xelatex --lua-filter=hebrew_inject.lua
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-- Hebrew Unicode ranges:
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-- U+05B0–U+05EA main block (letters + vowel points)
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-- U+FB1D–U+FB4F Hebrew presentation forms (rare but included)
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local function is_hebrew(cp)
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return (cp >= 0x05B0 and cp <= 0x05EA)
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or (cp >= 0xFB1D and cp <= 0xFB4F)
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end
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local function str_has_hebrew(s)
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local ok, result = pcall(function()
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for _, cp in utf8.codes(s) do
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if is_hebrew(cp) then return true end
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end
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return false
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end)
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return ok and result
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end
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-- Split a plain string into a list of pandoc Inlines,
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-- wrapping each Hebrew run in RawInline latex \heb{}.
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local function split_into_inlines(s)
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local parts = {}
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local run = {}
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local in_heb = false
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local function flush()
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if #run == 0 then return end
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local chunk = table.concat(run)
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if in_heb then
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table.insert(parts, pandoc.RawInline("latex", "\\heb{" .. chunk .. "}{}"))
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else
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table.insert(parts, pandoc.Str(chunk))
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end
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run = {}
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end
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for _, cp in utf8.codes(s) do
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local h = is_hebrew(cp)
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if h ~= in_heb then
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flush()
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in_heb = h
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end
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table.insert(run, utf8.char(cp))
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end
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flush()
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return parts
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end
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-- In a math string, replace \text{<content>} where <content> contains Hebrew
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-- with \text{{\hebrewfont <content>}}.
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-- Uses %b{} to correctly match balanced braces one level deep.
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local function inject_math_hebrew(s)
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return (s:gsub("\\text(%b{})", function(braced)
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local inner = braced:sub(2, -2) -- strip outer { }
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if str_has_hebrew(inner) then
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return "\\text{{\\hebrewfont " .. inner .. "}}"
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else
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return "\\text" .. braced
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end
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end))
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end
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-- Also handle bare Hebrew chars that appear directly in math (outside \text),
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-- e.g. $א$ — wrap them in {\hebrewfont X}.
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local function inject_bare_math_hebrew(s)
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local parts = {}
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local run = {}
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local in_heb = false
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local function flush()
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if #run == 0 then return end
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local chunk = table.concat(run)
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if in_heb then
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table.insert(parts, "{\\hebrewfont " .. chunk .. "}")
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else
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table.insert(parts, chunk)
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end
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run = {}
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end
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local ok = pcall(function()
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for _, cp in utf8.codes(s) do
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local h = is_hebrew(cp)
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if h ~= in_heb then
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flush()
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in_heb = h
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end
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table.insert(run, utf8.char(cp))
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end
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end)
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if not ok then return s end
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flush()
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return table.concat(parts)
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end
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-- ── Pandoc filter entry points ────────────────────────────────────────────────
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function Str(el)
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if not str_has_hebrew(el.text) then return nil end
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local parts = split_into_inlines(el.text)
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-- If there's only one part and it's already a plain Str, no change needed.
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if #parts == 1 and parts[1].tag == "Str" then return nil end
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return parts
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end
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function Math(el)
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if not str_has_hebrew(el.text) then return nil end
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-- First pass: handle \text{<hebrew>}
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local s = inject_math_hebrew(el.text)
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-- Second pass: handle any remaining bare Hebrew (not inside \text)
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-- We do this only outside already-processed \text{{\hebrewfont ...}} blocks.
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-- Simple heuristic: if the string still contains a raw Hebrew codepoint, wrap it.
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if str_has_hebrew(s) then
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s = inject_bare_math_hebrew(s)
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end
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if s ~= el.text then
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el.text = s
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return el
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end
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end

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