Chromatin / histone structural machinery — bottom-up mapping to the srmech genome¶

Research note (2026-07-18). A scoping/research pass (concertmaster dispatch): decompose the chromatin structural machinery (histones, euchromatin/heterochromatin, histone code, higher-order architecture, remodelers, accessibility) and read what the srmech genome layer already is vs. what a genuine gap would be. This is FORM-matching only — biology's X has the same cascade-shape as srmech's Y; it does not validate/prove/extend the framework, and biology is not superseded ([[user_stance_cascade_matching_substrate_blind_form_not_identity]]). Provisional throughout — candidates, not decisions. No code changed; no marker committed; no ADR. Companion to subharmonic_chirality_carrier_findings.md. Scope: organization-side algebra (which regions are reachable, compaction ratios, combinatorial masks, partition topology) — not the physical winding geometry (CAD-scope-banned).

1. What srmech already has (the rc268/rc269 chromatin layer)¶

Read from docs/srmech/python/srmech/amsc/genome.py + CHANGELOG.md [0.9.0rc268]/[rc269]/[rc272]:

CHROMATIN_MARKER = 0x48 ('H', histone/heterochromatin), format v14→v15 — an interior cap (like the 0x58 centromere it never opens a chromosome). Wire form (genome.py:285, :1790): [0x48] + handle + NUL + chromatin_type(uint8) + num(uint64 BE) + den(uint64 BE).
Accessibility level = one exact rational num/den ∈ [0,1] (Class-N; no float, never abs(); _validate_chromatin_level :1750). CHROMATIN_TYPE_BINARY = (1,1) open / (0,1) condensed; CHROMATIN_TYPE_GRADED = an arbitrary reduced rational (partial access). genome.py:288-301.
The ops — in-place, no re-mint (the "modify-without-re-mint" property): condense() (:1893) byte-splices the marker in, decondense() (:1947) splices it out, preserving centromere + body; chromatin_of() (:1962) reads back {type, state, level, handle, at, scope} or None (all-euchromatin default). Placement = scope: right after the opening telomere → whole-chromosome (the X-inactivation case); deeper interior → a sub-region stretch.
The OUTER gate expressed = accessible(region) AND promoter(gene, cell_state): wired into gene_express (:2407-2425), gene_express_levels (:2494-2512), the strand plan, and — rc269 — the demand-load PATH plan _gene_express_plan_path (:6325-6379). Heterochromatin silences a region even when its promoter would fire; a GRADED level composes multiplicatively with the §132 promoter level (_compose_levels, :2524, exact rational). The accessible predicate is Class-K: access_open = level_numerator > 0 (:2422).
rc269 bounded-I/O skip: at a region head the plan recognises a HEAD chromatin cap; condensed ⇒ the whole region is SKIPPED at plan time having touched ONLY the chromatin cap (its gene gate is never read). This is the load-bearing prior art for §876.
Adjacent machinery already present: combinatorial gene gates — klein4-mask 0x67, boolean-DNF 0x62, threshold/perceptron 0x77, graded 0x64 (:4770-4830); centromere 0x58 (mint-time global-chirality anchor); telomeres; and the out-of-core spectral partition recursive_cut → community tomes (laplacian.py:5906) with rc272 genome_partition/genome_from_graph reading nuclear-core vs plasmid-periphery from participation topology.

2. Biology → framework mapping (HAVE / PARTIAL / GAP / MISSING)¶

#	Biology structure	Cascade-shape (form)	srmech element	Status	Attested source
1	Nucleosome — octamer 2×(H2A/H2B/H3/H4), DNA wrapped ~1.65–1.7 left-handed turns for the canonical particle only; H1 linker; 10 nm "beads-on-a-string". ⚠ NOT a fixed quantum — see §2.1	quantized grouping of data units into one packaging/positioning quantum, keyed on the integer contact count k (attested 14), not on a turn decimal	`turn` = one Klein-4 leaf (2 bits ≈ one base-pair); chromosomes/tomes group turns — but no grouping quantum between datum and domain	GAP (missing rung)	Hodges et al. 2015 Genetics PMC4512544 (14 contacts, attested); McGinty & Tan 2014 Chem Rev PMC4378457 (147 bp; dyad-on-a-bp); MBoC NBK26834. Amended 2026-07-19 — see §2.1
2a	Euchromatin vs heterochromatin — open/transcribed vs condensed/silenced	binary/graded access gate over a region	`condense`/`decondense`/`chromatin_of`; the OUTER gate in `gene_express*`	HAVE	MBoC NBK26834 (histone code); NBK21137 Genomes "Accessing the Genome" (OA)
2b	Constitutive het (permanent — centromeres/telomeres, H3K9me3/HP1)	structural, mint-time, cell-state-invariant silence tied to structural landmarks	centromere `0x58` + telomere markers already are the constitutive anchors; chromatin `(0,1)` can pin them	PARTIAL	NBK21137; Chadwick & Willard 2004 PNAS PMC534659 (OA)
2c	Facultative het (context-dependent — Barr body / X-inactivation, H3K27me3/Polycomb)	cell-state-conditional access — the access layer itself responds to state	chromatin level is statically stored; it is NOT itself a function of `cell_state` (only the gene gate is)	GAP	NBK45037 (OA); Chadwick & Willard 2004 (OA)
3	Histone code — combinatorial PTMs (acetyl/methyl/phospho/ubiq) read as a mask, no sequence change	a combinatorial mark-set a reader interprets → different kinds of silence/activation	combinatorial vocab EXISTS but at the gene-promoter layer (`0x67/0x62/0x77`); the chromatin cap carries a single scalar `num/den`	PARTIAL / GAP	MBoC NBK26834 (attested, fetched: "combinations… very large… convey a particular meaning"); Strahl & Allis 2000 / Jenuwein & Allis 2001 (paywalled-primary)
4	Higher-order — 10/30 nm fiber, loops, TADs (CTCF/cohesin insulators), chromosome territories; A/B compartments	spectral community partition with encoded insulator boundaries; genome-scale two-way split	`recursive_cut` communities/tomes; rc272 participation split (≈ A/B compartments)	PARTIAL (communities HAVE; insulator marker MISSING)	Dixon 2012 Nature PMC3356448; Lieberman-Aiden 2009 Science PMC2858594; Cremer & Cremer 2010 CSHPB (OA) — all PMCID-cited, not PDF-verified this pass
5	Chromatin remodelers (SWI/SNF, ISWI, CHD, INO80) — ATP-driven nucleosome repositioning = active WRITE	an energy-gated actuator that writes the access layer	`condense`/`decondense` ARE the write-op; the ATP/energy budget = MFO EPH power source (F1059) is not modeled	HAVE (write) / MISSING (energy gate)	Clapier & Cairns 2009 Annu Rev Biochem 78:273-304 (paywalled-primary; training-attribution)
6	Accessibility as index — nucleosome-free promoters, DNase-HS / ATAC-seq; the accessibility landscape	cell-state-indexed distributed TOC — where the open regions are IS "where is what"	rc269 chromatin-gated demand-load plan = the mechanism, but not named/exposed as the §876 index	PARTIAL (latent)	Klemm, Shipony & Greenleaf 2019 Nat Rev Genet 20:207-220 (OA PDF + PMID 30675018); Buenrostro 2013 Nat Methods PMC3959825

2.1 AMENDMENT (2026-07-19) — the nucleosome wrap is NOT a fixed quantum¶

Supersedes the "fixed-ratio ~147-unit quantum / 1.65 turns" framing in row 1 above and in G3 below. Source: nucleosome_turn_asymmetry_frame_spike.md (concertmaster spike, this directory), which ran the question "what exact rational is 1.65?" to ground. Every claim here is OA-attested; the full attestation ledger and the generating script live with that note.

The finding: there is no fixed value to encode. The literature spread is not measurement scatter:

particle class	wrapped bp	turns	source
H2A.B nucleosome	103	1.2	PMC7780145
H3–H4 octasome	~120	1.5	PMC9659345
canonical NCP	145–147	1.65–1.7	PMC4378457
chromatosome (+H1)	166–167	1.9	PMC7801413

Further: the in vivo wrap ranges ~100–170 bp; salt-dependent unwrapping runs 7 ± 2 → 22 ± 5 bp across physiological ionic strength [PMC8129070]; ΔLk per nucleosome varies −1.4 … −0.9 as a systematic function of nucleosome spacing [PMC5659657]; and the handedness itself inverts (−0.80 ↔ +0.86 turns, barrier ~2.3 k_BT), with wrapping orientation set by the DNA's pre-assembly supercoiling state — not by the octamer [PMC4623960, PMC7959483]. Farr et al. name nucleosomes "a dynamic family of particles", not "static building blocks" [PMC8129070]. Luger et al. 1997's own abstract already said the DNA "deviate[s] from ideal superhelix geometry".

The honest object is a distribution, not a constant.

Tooling consequence for srmech (the srmech-side content, and the only part this note decides):

The GAP in row 1 / G3 still stands — srmech's ladder still jumps from datum (turn ≈ bp) straight to domain, with no packaging/positioning rung. That is unchanged.
But any future quantisation rung must key on the INTEGER contact count k, never on a turn decimal or a fixed bp count. The attested discrete invariant is 14 minor-groove-inward contacts at SHL −6.5…+6.5, one arginine each [Hodges et al. 2015, PMC4512544]. The bp figure is a projection of k under a periodicity that itself varies; the turn count is a projection of a projection. A rung parameterised on "147" or "1.65" would be encoding a rounding of one crystal structure as a constant.
Corollary for the marker design: a grouping quantum should carry k (a small integer) and derive span, rather than store a span and imply k. This also makes sub/super-nucleosomal particles (hexasome k=11, tetrasome, chromatosome k=16) expressible in the same vocabulary instead of as exceptions.
Do not encode ΔLk = −1.0. That value is a postulate; the measurement is −1.26 [PMC6162219], and it varies with spacing. If a topological field is ever added, it is a distribution parameter.

Ontological point — MFO-side, cross-ref only (not restated here per [[feedback_mfo_vs_srmech_notebook_split_rule]]): that the deviation is itself content rather than error, and that the honest object is a distribution, is substrate/ontology material. See nucleosome_turn_asymmetry_frame_spike.md §2–§4 and the MFO fermata recorded there. This note does not adjudicate it.

3. The compaction hierarchy mapped onto srmech¶

Biology's compaction ladder is a nested set of quanta; srmech's ladder skips the nucleosome/fiber rungs and jumps from datum straight to domain. The access marker (0x48) rides beside the ladder as a gate, not as a rung.

graph TD
  subgraph BIO["biology compaction ladder (nested quanta)"]
    bp["base pair (2 bits, 4 nt)"]
    nuc["NUCLEOSOME  k=14 contacts  (octamer quantum)<br/>span 100-170 bp / 1.2-1.9 turns = a DISTRIBUTION"]
    f10["10 nm  beads-on-a-string"]
    f30["30 nm fiber (in-vivo existence contested)"]
    loop["loop / TAD  (CTCF+cohesin insulated)"]
    comp["A / B compartment  (open / closed)"]
    terr["chromosome territory"]
    bp --> nuc --> f10 --> f30 --> loop --> comp --> terr
  end
  subgraph SR["srmech ladder"]
    turn["TURN = Klein-4 leaf (2 bits) ~ base pair"]
    QMISS["(no packaging/positioning QUANTUM)"]
    FMISS["(no fiber rung)"]
    chrom["chromosome / kernel strand"]
    tome["community / tome (recursive_cut, Fiedler)"]
    part["nuclear-core vs plasmid (rc272 participation)"]
    cell["genome / cell registry"]
    turn --> QMISS -.MISSING.-> FMISS -.MISSING.-> chrom --> tome --> part --> cell
  end
  nuc -. "GAP: quantized grouping rung" .- QMISS
  loop -. "insulator marker MISSING; boundary derived not encoded" .- tome
  comp -. "≈ Fiedler two-way split (HAVE)" .- part
  bp -. "turn ≈ base pair (2 bits = 4 nt)" .- turn
  classDef miss fill:#fdd,stroke:#c00;
  class QMISS,FMISS miss;

ASCII (the access gate rides beside the ladder):

 biology:  bp --> [NUCLEOSOME k=14 contacts] --> 10nm --> 30nm --> loop/TAD --> A/B --> territory
                   ^ span 100-170bp / 1.2-1.9 turns: a DISTRIBUTION, not a constant (see 2.1)
 srmech :  turn --> ( . . . missing quantum . . . )        -->  chromosome --> tome --> nuclear/plasmid --> cell
                                                                     ^recursive_cut       ^rc272
           access layer (0x48 chromatin):  euchromatin/heterochromatin gate  ==  A/B compartment state
                                            (rides beside the ladder as a mask, not as a rung)

Reading of the ladder: turn ≈ base pair, chromosome/tome ≈ loop/TAD, rc272 participation split ≈ A/B compartment, registry ≈ territory/cell. The two skipped rungs (nucleosome quantum, fiber) are the structural gaps; the insulator boundary is derived-not-encoded.

4. Genuine gaps & candidate primitives (ranked)¶

G1 — Facultative heterochromatin: the access layer is not cell-state-conditional. [highest] Biology's facultative het (Barr body / X-inactivation) is cell-state-dependent silence — the access layer itself responds to state. srmech's chromatin level is statically stored; only the gene gate reads cell_state. Cascade-shape it fills: a state-indexed access landscape (the same genome ⇒ a different open-set per state). Candidate (not a decision): let the chromatin cap carry (or reference) a gate — reuse the existing gene-gate klein4/DNF/threshold machinery on the chromatin cap so accessible(region, cell_state) is computed, not stored. The machinery already exists one layer down; wiring it onto 0x48 would make constitutive = unconditional (0,1) (or tied to 0x58/telomere) and facultative = a state-gated cap. This is the find→FIX candidate: the parts are in the box.

G2 — Histone code is combinatorial; the chromatin cap is a single scalar. [high] Biology's histone code is a mark-SET (H3K9me3+HP1 → constitutive silence; H3K27me3 → facultative silence; H3K4me3 → active promoter; H3K27ac → active enhancer) — different marks encode different kinds of state with different reversibility. srmech collapses all of it to one accessibility rational, which cannot distinguish constitutive from facultative (both are (0,1)). Candidate: extend chromatin_type beyond BINARY/GRADED to a small combinatorial mark-set, or minimally a CONSTITUTIVE/FACULTATIVE type byte (composes with G1). Blue-team caveat: do not over-model — biology's "code" is partly interpretive/context; a full mark alphabet risks scope creep. The minimal honest step is the constitutive/facultative distinction, which G1 already implies.

G3 — Nucleosome as a quantized grouping/positioning rung. [high, but scope-fenced] — AMENDED 2026-07-19 srmech's ladder skips from datum (turn ≈ bp) straight to domain; biology inserts the nucleosome — a quantum that is (a) the unit at which access is granted, (b) the substrate the histone-code mask attaches to, © positioned by a code (Segal 2006). Cascade-shape it fills: a regular grouping grid on which accessibility is defined (today condense(region=…) takes an arbitrary data-turn index or gene label — no grid). Candidate: a positioning/grouping quantum as the addressable unit of access.

⚠ AMENDED — the quantum is NOT fixed-N (§2.1). The original "fixed-N (~147-unit)" framing is superseded. The wrap is a distribution (100–170 bp in vivo; 1.2/1.5/1.65–1.7/1.9 turns across four attested particle classes; handedness even inverts). The rung must key on the integer contact count k (attested 14), not on a fixed span or a turn decimal — see §2.1 items 2–3. This strengthens rather than weakens G3: keying on k makes hexasome/tetrasome/chromatosome first-class in the same vocabulary instead of exceptions to a constant.

Scope fence (unchanged): the physical winding geometry is out of scope for mesh/FEA/tolerance GPU simulation; the in-scope object is the information-organization quantum (grouping + positioning grid), not the spool. Note per [[feedback_cad_ban_is_gpu_numerical_not_closedform_physical]] the closed-form topology/algebra of the winding is in scope — that is how §2.1's numbers were derived.

G4 — Insulator / TAD-boundary marker (CTCF/cohesin). [medium] recursive_cut finds community boundaries by spectral min-cut (derived); biology encodes boundaries (convergent CTCF sites, cohesin loop-extrusion stops). srmech has no insulator marker — a boundary is computed, never stored/pinned. Cascade-shape: a Class-K pin at a partition boundary (a boundary analog of the 0x58 centromere pin). Candidate: an insulator cap that constrains/pins a recursive_cut boundary (a TAD edge). Ties loop-extrusion (an active motor) to the EPH-propagator picture.

G5 — Remodeler write is energy-free; biology gates the write behind ATP. [low, resonance] condense/decondense = the remodeler write, but the write is "free." Biology's remodeler is ATP-driven = the MFO EPH power source (F1059, "inference IS photosynthesis"). Observation, not a must-fix: if srmech ever models the EPH energy budget, the access-layer write is exactly where the ATP cost attaches — the remodeler is the WRITE side of the access gate powered by that engine.

5. What the literature surfaced OUTSIDE the three named structures¶

Finding	Why load-bearing	Maps to	Attestation
A/B compartments (Hi-C) — genome-scale open(A)/closed(B) split = leading eigenvector of the contact matrix	euchromatin/heterochromatin IS a two-way spectral split → directly `fiedler_sparse` / rc272 participation	G-none (RESONANCE — strengthens §4 higher-order)	Lieberman-Aiden 2009 Science 326:289 PMC2858594 (PMCID-cited, not PDF-verified)
TAD / CTCF / cohesin loop-extrusion	boundaries are encoded, not derived	G4 insulator marker	Dixon 2012 PMC3356448; Fudenberg 2016 / Sanborn 2015 (PMCID, not verified)
Nucleosome positioning code	where nucleosomes sit sets default access — a quantized positioning grid	G3 positioning grid	Segal 2006 Nature 442:772 (paywalled-primary; training-attribution)
Phase-separation / condensate heterochromatin (HP1)	heterochromatin as a phase-separated compartment, not a linear mark ≈ a dense spectral cluster / condensate = the recursive_cut community	reframes G4/A-B: the community IS the "condensate"	Strom 2017 / Larson 2017 Nature (paywalled-primary; OA repo escholarship 3vh8n30c)
Replication timing (early=euchromatin, late=heterochromatin)	a genome-wide ordering coupled to accessibility = a natural coherency-ORDER for the §876 reader	the accessibility state implies a read-order	textbook / review (unattested this pass — FLAG)
Histone variants (CENP-A, H2A.Z, H3.3)	CENP-A is the centromere-defining variant → already srmech's `0x58`; H2A.Z at boundaries	reinforces constitutive=`0x58`; minor variant-type axis	MBoC / reviews (unattested this pass — FLAG)
DNA methylation (5mC / CpG)	an epigenetic mark on the datum strand itself, not a cap — a distinct axis srmech has no analog for	possible per-turn mark axis (distinct from cap-level access)	reviews (unattested this pass — FLAG)

6. The §876 connection (highest-value)¶

The accessibility landscape as the distributed index is the strongest finding. Biology has no plain-text TOC; where the open regions are, at a given cell-state, is "where is what" (Klemm/Greenleaf 2019). srmech's rc269 chromatin-gated demand-load plan already implements this mechanism — condensed regions are skipped at plan time, so the euchromatin regions ARE the plan — but it is not yet named/exposed as the §876 distributed index, and it is not yet cell-state-indexed at the access layer (that needs G1). Combined with A/B compartments (the index is a spectral split) and replication timing (the index implies a read-order), the picture for §876 is: an accessibility_landscape(genome, cell_state) read = the distributed TOC = the EPH "find" seed-set, computed by walking the 0x48/gate caps in coherency order and exploding to RAM only the open subset (exactly the project_genome_streaming_reader_eph_universal design). The mechanism exists; the framing and the cell-state-conditional access layer are the missing pieces.

7. Open questions for the user (fermatas — this pass is NOT authorized to decide)¶

F-a (unified frame vs separate layers). G1-G4 all add cap kinds. Does the marker alphabet stay byte-per-layer (13→N markers), or does the incoming chromatin/insulator layer force the codon-radix k=3 unified-frame decision (project_genome_framing_codon_radix_k3)? ~~Note: nucleosome core 147 bp = 3×49 = exactly 49 codons…~~ WITHDRAWN 2026-07-19 (§2.1). That observation rested on 147 bp being a constant. It is not — the wrap is a distribution (100–170 bp), and 147 is one crystal construct's value. A "49 codons exactly" coincidence computed from a non-constant is not an anomaly, weak or otherwise. Do not revive it without a fixed span to compute from. The F-a question itself (byte-per-layer vs unified k=3 frame) stands on its own merits, untouched by this withdrawal.
F-b (facultative gate placement). For G1, does the chromatin cap carry its own gate, or reference a shared gate table? (Carry = self-describing per §44; reference = DRY but adds indirection.)
F-c (how far to take the histone code). G2 minimal = a constitutive/facultative type byte; maximal = a combinatorial mark alphabet. Where is the honest stopping point vs over-modeling an interpretive code?
F-d (insulator vs centromere). Is the G4 insulator a new cap, or a reuse/parameterization of the 0x58 centromere pin (both are Class-K structural pins, but one is a boundary, one an origin)?
F-e (attestation upgrades). Several §5 rows are PMCID/training-attribution only. Which mappings does the user want PDF-verified before any of this leaves a scoping note (per MPM)?

8. Sources (attestation status)¶

Attested (OA, verified this session): - Alberts B, Johnson A, Lewis J, Raff M, Roberts K, Walter P. Molecular Biology of the Cell, 4^th ed. (Garland Science, 2002), "Chromosomal DNA and Its Packaging in the Chromatin Fiber," NCBI Bookshelf NBK26834 — WebFetch-verified: octamer 2×(H2A/H2B/H3/H4), 146 bp, wrapped 1.65 turns left-handed, (these are the values that source states, recorded verbatim; 146 is superseded by 147 and 1.65 is canonical-particle-only, not a constant — see §2.1), H1 linker, beads-on-a-string, histone-tail modifications + combinatorial "histone code" proposal. - Chadwick BP & Willard HF (2004) "Multiple spatially distinct types of facultative heterochromatin on the human inactive X chromosome," PNAS 101:17450, PMC534659 (OA) — facultative het / Barr body. - Klemm SL, Shipony Z & Greenleaf WJ (2019) "Chromatin accessibility and the regulatory epigenome," Nat Rev Genet 20:207-220, PMID 30675018 (OA institutional PDF located) — accessibility landscape. - Genomes (T.A. Brown), "Accessing the Genome," NCBI Bookshelf NBK21137 (OA) — euchromatin/ heterochromatin, constitutive vs facultative (ID confirmed; exact-quote not fetched this pass).

Landmark — paywalled primary / OA-corroborated fact or OA-secondary (flagged): - Luger K, Mäder AW, Richmond RK, Sargent DF, Richmond TJ (1997) "Crystal structure of the nucleosome core particle at 2.8 Å resolution," Nature 389:251-260, PMID 9305837 — paywalled at Nature; the 146/147 bp + 1.65-turn fact is independently OA-attested via NBK26834. - Strahl BD & Allis CD (2000) Nature 403:41; Jenuwein T & Allis CD (2001) Science 293:1074 — histone code; paywalled-primary; concept OA-attested via NBK26834. - Clapier CR & Cairns BR (2009) "The biology of chromatin remodeling complexes," Annu Rev Biochem 78:273-304 — paywalled (Annual Reviews); training-attribution, not verified this pass. - Lieberman-Aiden E et al. (2009) Science 326:289 (A/B compartments), PMC2858594; Dixon JR et al. (2012) Nature 485:376 (TADs), PMC3356448; Cremer T & Cremer M (2010) CSH Perspect Biol (territories, OA); Segal E et al. (2006) Nature 442:772 (positioning code, paywalled); Strom AR et al. / Larson AG et al. (2017) Nature 547 (phase separation, paywalled-primary, OA repo exists); Buenrostro JD et al. (2013) Nat Methods 10:1213 (ATAC-seq), PMC3959825 — all PMCID/PMID-cited, NOT PDF-verified this pass.

Unattested this pass (FLAGGED — do not rest a mapping on without verification): replication-timing / accessibility coupling; histone-variant specifics (CENP-A/H2A.Z/H3.3); DNA methylation (5mC/CpG).

Cross-links: nucleosome_turn_asymmetry_frame_spike.md (2026-07-19 — the amendment in §2.1 / G3 comes from there; also carries the Lk=Tw+Wr frame analysis, the k=3 reading, and the MFO-side fermata F-g); rc268/rc269 CHANGELOG; project_genome_streaming_reader_eph_universal; project_genome_framing_codon_radix_k3; user_stance_cascade_matching_substrate_blind_form_not_identity; feedback_no_lineage_claims_in_notebook; feedback_mfo_vs_srmech_notebook_split_rule; feedback_cad_ban_is_gpu_numerical_not_closedform_physical.