research: centre sink duality, dependent-triple braid sparsity (|B| <= 12), and circle-cancellation sharing ceilings

[dcharb78]

Research Package: Centre Sink Duality, Dependent-Triple Braid Sparsity ($|B| \le 12$), and Circle-Cancellation / Role-Untangled Sharing Ceilings (centre-path-sharing)

1. Selected-Result vs Archival Base Status & Priority Card Alignment

• Selected record (certificates/selected-result.json, #1094): Validated repository baseline with $\kappa = 0.001672660197076918$ (intake_status.classification = "validated"). This pull request adds the self-contained research package research/centre-sink-duality-and-braid-quotient/ supplying an exact structural audit, lower bound, and fully charged ceiling stratification for the 64-per-call centre path; no new global $\kappa$ is claimed.
• Pinned verification inputs (SOURCES.json) and prior centre-sharing lineage built upon here: The decompressed replay archive research/community-frontier1094-audit/selected-replay.tar.gz, the packing-independent local-word ceiling solver research/complex-local-word-ceiling/ceiling.py and RESULT.json (#1012 coverage lineage), and the two-panel reverse centre-phase guard certificate research/centre-shared-return-guard/RESULT.json (#1748, complementary to #1708) constitute the pinned verification inputs in SOURCES.json at base_commit = 997e6a9ca7b4f95d50e366f61412fd640d72a88a. While verify.py computes all matrices and censuses directly from selected-replay.tar.gz (so no files from #3071, #3075, #3097, or #3120 are read at runtime), this package builds directly on the problem formulations, structural theorems, and open questions of #3071 (research/centre-block-repair-information, Ross Richardson, merged_for_archive_only, partially_reviewed), #3075 (research/centre-shared-kcall-charged-seed615415, Aaron Wang / navinor, merged_for_archive_only, partially_reviewed), #3097 (research/centre-seven-owner-information-floor, Gonzalo-Mier, merged_for_archive_only, partially_reviewed), open PR #3120 (research/centre-demand-rank-floor, Aaron Wang / navinor), research/centre-owner-observation-floor (ywz65), research/centre-sharing-overhead-budget (rtyu193-rgb), and research/selected-centre-quarter-native (navinor, #2199 Sagar Thakrar), where each archived or open PR reports (author-checked) its respective theorem, table, or scan.
• Priority card alignment (docs/research/current-priorities.md and docs/research/agent-task-catalog.json, revision 6): Targets track recursive-interfaces (20% portfolio weight), card centre-path-sharing: "Can the 64-per-call centre path (eight rank-8 COPY/ERASE totals through the private temporary) be shared across calls or shrunk?" (chooser_seed = "d78c20261017ce000000000000000001", scope_status = "unchanged").

---

2. Summary of the Four Verified Pillars (PASS_CENTRE_SINK_DUALITY_AND_BRAID_QUOTIENT)

Running python3.12 -B research/centre-sink-duality-and-braid-quotient/verify.py deterministically verifies four self-contained pillars directly from the 4 pinned upstream inputs in ~5.4 seconds using Python 3.12 standard library only:

1. Pillar 1 — Physical Sink Decoding across Both split-centres (728 Roles) and hosted (gauge44, 704 Roles) Templates (1152 / 1152 Resolved, 0 Missing):

   • Resolves the apparent 16 present / 1136 missing (1,136 missing) lookup failure reported (author-checked) by external comparator #3120 (research/centre-demand-rank-floor). In both decompressed templates, call["owners"] is a positional list indexed by local role 0..727 (split-centres) or 0..703 (hosted), where each entry [owner_id, chart] maps local role $r$ to its global owner ID p[0] and chart p[1].
   • Indexing call["owners"] as a dictionary {p[0]: p[1]} keyed by global owner ID p[0] and querying the local helper indices S_split = (229, 224, 227, 225, 243, 241, 259, 257) succeeds only when a call's global owner IDs happen to lie in 224..259 — which occurs exclusively in Replica 0, Pair 1 (1*224 .. 1*224+111 = 224..335), namely Call 48 (Stage 3, backward) and Call 64 (Stage 4, forward) at local data roles [5, 0, 3, 1, 19, 17, 35, 33], yielding 16 present and 1136 (1,136) missing lookups (Negative Control 1).
   • Positional indexing call["owners"][s] resolves 1152 / 1152 (1,152 / 1,152, 0 missing) in both templates:
     • In split-centres (728 roles, 21,483 events, 28 fanout/gather steps per centre), the 8 post-$A$ source/sink roles are S_split = (229, 224, 227, 225, 243, 241, 259, 257) (owner_id in 14,336..22,939, chart [2, rep % 8]). Because odd stages (1, 3, 5, 7) and even stages (0, 2, 4, 6, 8) use disjoint helper owner pools and chart = [2, rep % 8] separates the 8 replicas sharing each helper pool, 0 of 10,296 call pairs share both (owner_id, chart) and 0 of 576 same-replica pairs share any owner_id.
     • In hosted (gauge44, 704 roles, 24,767 events, 208-event centre window 12,551..12,758, 22 fanout/gather steps per centre), the 8 post-$A$ source/sink roles are S_hosted = (92, 57, 81, 224, 11, 240, 9, 256), which split into 5 Data Sinks S_data = (92, 57, 81, 11, 9) (720 lookups, chart [1, stage, port]) and 3 Helper Sinks S_helper = (224, 240, 256) (432 lookups, chart [3, bank, offset]).

2. Pillar 2 — Three Exact 704-Role Forward/Backward Duality Laws & Complete 10,296-Pair Guard and Demand-Coupling Census:

   • Across all $k \in {0..7}$ and all $704$ local roles of the decompressed hosted (gauge44) forward (WORD-forward.json.gz) and backward (WORD-backward.json.gz) words (Negative Control 2):
     $$\text{bwd_cut}[k, 112+p] = (+1)\cdot\text{fwd_resp}[k, 112+p], \quad \text{bwd_cut}[k, 112+p] = \left(+\frac{1}{4}\right)\cdot\text{fwd_cut}[k, p] \quad (\forall p \in {0..111}),$$
     $$\text{fwd_cut}[k, i] = (-1)\cdot\text{bwd_resp}[k, i] \quad (\forall i \in {0..703}).$$
   • Each forward pre-centre cut row fwd_cut[k] (and -bwd_resp[k]) is supported on all 112 data roles 0..111 ($D$), 0 panel roles 112..223 ($T$), and 115 helper roles inside 224..447 ($H$), while bwd_cut[k] (and fwd_resp[k]) is supported exclusively on the 112 panel roles 112..223 ($T$), with 22 immediate panel steps of $\ell_1$-norm $11/2$ inside the 208-event centre window expanding to 56 target rows after Phase B.
   • Evaluating the 5 physical guard conditions across all $\binom{144}{2} = 10{,}296$ call pairs (143 adjacent schedule pairs) establishes a Two-Regime Dichotomy:
     • Regime I (1080 / 1,080 Cross-Replica Same-Stage Pairs): Satisfy same_orient = True, panel_overlap = 0, relative route $\rho_{\text{rel},p} = I$, and high chart alignment ({5: 889, 6: 157, 7: 22, 8: 12} matching sink charts), yet share 0 / 5 Data Sinks (0 pairs) and at most 1 / 3 Helper Sink (3 same-stage pairs; 18 pairs with same_orient = True, disjoint panels, and chart_slot_matches in {0, 5, 6}, 19 across all same_orient = True disjoint-panel pairs, and 26 across same_orient = False disjoint-panel pairs), with joint data rank $8 + 8 = 16$ and demand-coupling rank $2$.
     • Regime II (96 Same-Replica Shared-Data Pairs, 6 per Replica $\times 16$ Replicas): Share all 224 $D \cup T$ owners and all 5 / 5 Data Sink owners (92, 57, 81, 11, 9) (93 pairs share 0 Helper Sinks — including every Replica 0 pair and all 16 same-orientation f0 -> f2 pairs — and 3 opposite-orientation pairs share 1 Helper Sink), and have chronological joint source rank $8$ on $D_{\text{pair}}$ (demand_coupling_rank = 1), split into 16 pairs in each of the 6 stage classes f0->b1, b1->f2, f0->f2, b3->f4, b5->f6, and b7->f8.

3. Pillar 3 — Route-Product Order Census & Dependent-Triple Braid Sparsity Theorem (Closing $7 \le |B| \le 12$):

   • Extracts all 112 port route involutions $\rho_p \in O_{17}(\mathbb{F}2) \subset O{73}(\mathbb{F}_2)$ directly from DATA-PHASES.json. All $112 \times 111 = 12{,}432$ ordered products $\rho_p \rho_q$ ($p \neq q$) are distinct (Negative Control 3), and the $\binom{112}{2} = 6{,}216$ unordered pairs have exact order distribution {2: 0, 3: 50, 4: 1197, 5: 1040, 6: 959, 8: 290, 9: 1568, 12: 792, 17: 188, 20: 132}.
   • The 50 order-3 braid edges $(\rho_p \rho_q)^3 = I$ (where $\rho_p \rho_q \rho_p = \rho_q \rho_p \rho_q$) span 74 active vertices with maximum degree 6, 0 triangles, and 0 4-cycles (girth $\ge 5$).
   • Dependent-Triple Braid Sparsity Theorem: Checking all $\binom{112}{3} = 229{,}936$ port triples of the $8 \times 112$ pre-centre cut matrix $R$ in exact primitive integer arithmetic proves that $R$ has 896 linearly dependent triples, of which 846 contain 0 braid edges, 50 contain 1 braid edge (each of the 50 braid edges ${a, b}$ extends to a unique dependent triple ${a, b, c}$ via a port $c \in {77: 24, 78: 12, 79: 5, 80: 4, 81: 3, 82: 2}$), and 0 contain 2 or 3 braid edges.
   • Consequence (Block Floor $|B| \ge 13$, Closing $7 \le |B| \le 12$): In any 1-to-1 two-stage block-repair incidence graph $I = (B, D_{\text{act}}, E)$ with minimum degree $\ge 3$ and no 4-cycles (since $\rho_a \rho_b$ never has order 2), every 6-cycle requires a braid edge ${a, b}$ at its incident vertices and uniquely determines the remaining two $B$-vertices as $g(\rho_a \rho_b)$ and $g(\rho_b \rho_a)$. Because a degree-3 vertex $v \in B \cup D_{\text{act}}$ has port support of size 3 that must be linearly dependent in $R$ (or $H = R/4$), its support contains at most 1 braid edge and therefore lies in at most 1 six-cycle (while a vertex of degree $k \ge 4$ lies in at most $\lfloor k^2/4 \rfloor$ six-cycles by Mantel's theorem on the triangle-free braid graph). Across all 7 <= |B| <= 12 (closed_block_floor_max_B = 12), the forced non-claw triangles in the distance-2 graph $G_2(B)$ strictly exceed this capacity (0 feasible $C_4$-free degree partitions for $m \in {7, 8, 9, 10, 11, 12}$), whereas relaxing the degree-3 limit to the abstract $C_4$-free Fano incidence count $3(3-1)^2 = 12$ immediately admits the Fano $(3^7)/(3^7)$ partition at $m = 7$ (Negative Control 5).

4. Pillar 4 — Chronological $(F_0 \to B_1 \to F_2)$ Circle Cancellation, Stage-8 Zero-Feedback Circle, and Role-Untangled $k=2$ Ceiling Stratification via ceiling.ceiling(centre=...):

   • Chronological Replica 0 $(F_0 \to B_1 \to F_2)$ Circle Cancellation: Replaying the exact chronological window from Call 0 (f0, event 0) through Call 4 (b1, event 9) to Call 10 (f2, event 25) proves that only 3 stage-0 bridge events (2, 3, 4 on p1<->p2, p1<->p3, p2<->p3) intervene, leaving $D_0 \cup T_0$ (0..223) and all 5 Data Sinks untouched. By Duality Law 2, Call 4 (b1) writes $\Delta D_0 = -\frac{1}{4} R_D x^{(0)}$, which cancels Call 10's pre-centre demand $\frac{1}{4} R_D x^{(0)} + R_D \Delta D_0 = 0$ on $D_0$ (rank_D0_f2 = 0), while ablating Call 4 (b1) leaves rank_D0_f2 = 8 (Negative Control 6).
   • Stage-8 Zero-Feedback Circle ($9 = 8 + 1$ Macro Decomposition): In every replica, Stage 8 (Call 128 at schedule event 297 on Replica 0) is followed only by 16 terminal events (312..327) with 0 subsequent local_cover_sweep or bridge events, so its post-$B$ panel response has zero downstream feedback consumption.

---

3. Complete Summary Table of Verified Ceiling Brackets (ceiling.ceiling(centre=...))

All ceiling brackets $[a_{\text{lo}}, a_{\text{hi}}]$ and $\kappa_{\text{cap}} = a_{\text{hi}} / (1 + a_{\text{hi}})$ are certified on grid $10^{-12}$ via research/complex-local-word-ceiling/ceiling.py ($m = 73$, $\text{families} = 896$, $\text{stages} = 9$, $w = 896/9 \approx 99.555556$, $R = 51$):

Architecture / Sharing Regime	Effective Centre $C_{\text{eff}}$	Unpaid Deficit $D = 896/9 - C_{\text{eff}}$	Paid Local Profile {rank: count/call}	Certified $a_{\text{cap}}$ (or $a^*$)	Certified $\kappa_{\text{cap}}$	Ratio vs Baseline $a_{\text{cap}}$
Selected Baseline ($k = 1$)	64	320/9 (35.555556)	{1: 2412, 2: 418, 3: 432, 4: 142, 5: 82, 8: 8}	0.001690054110	0.001687202646	1.000000x
Stage-8 Zero-Feedback Circle ($9 = 8 + 1$)	512/9	384/9 (42.666667)	{1: 21692/9, 2: 418, 3: 432, 4: 142, 5: 82, 8: 64/9}	0.002029002668	0.002024894152	1.200555x
Same-Replica $(F_0 \to B_1 \to F_2)$ Circle Quotient ($\Delta H = 8/9$)	512/9	384/9 (42.666667)	{1: 21716/9, 2: 418, 3: 432, 4: 142, 5: 82, 8: 64/9}	0.002027990479	0.002023886057	1.199956x
Combined Stage-8 + $(F_0 \to B_1 \to F_2)$ Circle Quotient	448/9	448/9 (49.777778)	{1: 21700/9, 2: 418, 3: 432, 4: 142, 5: 82, 8: 56/9}	0.002367082582	0.002361492734	1.400596x
Role-Untangled $k = 2$ Window ($\Delta H = 0$, 1-bit guard)	32	608/9 (67.555556)	{1: 2408, 2: 418, 3: 432, 4: 142, 5: 82, 8: 4}	0.003215381840	0.003205076302	1.902532x
Role-Untangled $k = 2$ Window ($\Delta H = 8$, Displace)	32	608/9 (67.555556)	{1: 2416, 2: 418, 3: 432, 4: 142, 5: 82, 8: 4}	0.003210567561	0.003200292784	1.899683x
Role-Untangled $k = 2$ Window ($\Delta H = 8$, Additive)	40	536/9 (59.555556)	{1: 2416, 2: 418, 3: 432, 4: 142, 5: 82, 8: 4}	0.002831949289	0.002823951980	1.675656x
Role-Untangled $k = 2$ Window ($\Delta H = 16$, Displace)	32	608/9 (67.555556)	{1: 2424, 2: 418, 3: 432, 4: 142, 5: 82, 8: 4}	0.003205767701	0.003195523596	1.896843x
Role-Untangled $k = 2$ Window ($\Delta H = 16$, Additive)	48	464/9 (51.555556)	{1: 2424, 2: 418, 3: 432, 4: 142, 5: 82, 8: 4}	0.002449238366	0.002443254255	1.449207x
Role-Untangled $k = 2$ Window ($\Delta H = 24$, Displace)	32	608/9 (67.555556)	{1: 2432, 2: 418, 3: 432, 4: 142, 5: 82, 8: 4}	0.003200982193	0.003190768674	1.894012x
Role-Untangled $k = 2$ Window ($\Delta H = 24$, Additive)	56	392/9 (43.555556)	{1: 2432, 2: 418, 3: 432, 4: 142, 5: 82, 8: 4}	0.002067246243	0.002062981563	1.223183x
Role-Untangled $k = 2$ Window ($\Delta H = 31$, Additive Break-Even at $T_2$)	63	329/9 (36.555556)	{1: 2439, 2: 418, 3: 432, 4: 142, 5: 82, 8: 4}	0.001733590570	0.001730590435	1.025760x
Role-Untangled $k = 2$ Window ($\Delta H = 32$, Additive Break-Even at $a_{\text{selected}}$)	64	320/9 (35.555556)	{1: 2440, 2: 418, 3: 432, 4: 142, 5: 82, 8: 4}	0.001685970114	0.001683132402	0.997584x

• Break-Even Overhead Envelopes ($k = 2$):
  • Displace model (idle_mass absorbs $\Delta H$): feasible up to the coverage-identity cap $H = 1650$ (1,650 extra rank-1 operations per call) at both $T_2 = 24189832256 / 14320084696015 \approx 0.001689224107$ and $a_{\text{selected}} = 278488365152 / 166218993758335 \approx 0.001675460322$.
  • Additive model (centre increases by $\Delta H$): sharp break-even at $H = 31$ against $T_2$ (H = 31 passes with $a^* = 0.001733590570 &gt; T_2$, while H = 32 drops to $a^* = 0.001685970114 &lt; T_2$) and sharp break-even at $H = 32$ against $a_{\text{selected}}$ (H = 32 passes with $a^* = 0.001685970114 > a_{\text{selected}}$, while H = 33 drops to $a^* = 0.001638360802 < a_{\text{selected}}$).

---

4. Eight Behavioral Negative Controls Checked by verify.py

1. control_1_global_vs_local_owner_misindexing: Keying call["owners"] by global owner ID p[0] on S_split = (229..259) hits only Calls 48 and 64 (16 present / 1136 missing), whereas positional indexing resolves 1152 / 1152 (0 missing) in both split-centres and hosted.
2. control_2_duality_sign_and_quarter_perturbation: Perturbing any of the three exact duality ratios (+1, +1/4, -1) or omitting helper roles 224..447 falsifies the 704-role forward/backward duality laws.
3. control_3_collinear_or_duplicate_route_rejection: Injecting a parallel column into $R$ or a duplicate route involution into ${\rho_p}_{p=0}^{111}$ is immediately rejected (111 < 112).
4. control_4_collapsed_routes_zero_repair: Collapsing relative routes $\rho_{\text{rel},p} \to I$ reduces the two-call joint source rank on $D$ from $16$ to $8$ (0 repair coordinates required).
5. control_5_unconstrained_degree3_triangle_allowance: Relaxing the degree-3 six-cycle limit from 1 (forced by the Dependent-Triple Braid Sparsity Theorem) to the abstract $C_4$-free Fano incidence count 12 admits the Fano $(3^7)/(3^7)$ partition at $m = 7$ (1 feasible configuration), whereas the Dependent-Triple Braid Sparsity Theorem forces 0 feasible configurations across all $7 \le m \le 12$.
6. control_6_b1_ablation_destroys_f2_source_cancellation: Ablating Call 4 (b1) raises Call 10 (f2) pre-centre cut rank on $D_0$ from 0 to 8, destroying the $(F_0 \to B_1 \to F_2)$ circle cancellation.
7. control_7_pinned_bill_and_baseline_reproduction: The $k = 1$ and $k = 2$ window formulas reproduce the pinned separate (16 / 368 / 32) and fused (8 / 360 / 16) macro bills from research/centre-shared-return-guard/RESULT.json (#1748) and the baseline ceiling 0.001690054110 from research/complex-local-word-ceiling/RESULT.json (#1012 coverage lineage).
8. control_8_monotone_overhead_and_sharp_breakeven: Adding $+1$ rank-1 child or doubling the precision guard strictly lowers $a_{\text{cap}}$, and the additive break-even thresholds $H = 31$ (at $T_2$) and $H = 32$ (at $a_{\text{selected}}$) are verified sharp at $H$ vs $H + 1$.

---

5. Relationship to Prior Centre-Sharing Packages & Open PRs (#3071, #3075, #3097, #3120)

• #3075 (research/centre-shared-kcall-charged-seed615415, Aaron Wang / navinor): Reports (author-checked) a charged $k$-call relaxation table under merged_for_archive_only and partially_reviewed intake status and poses the open physical 144-call sink-sharing eligibility and demand-coupling classification questions. Pillar 1, Pillar 2, and Pillar 4 build on that relaxation framework, resolve those two open questions across all $10{,}296$ pairs, and add the chronological $(F_0 \to B_1 \to F_2)$ and Stage-8 circle-cancellation profiles.
• #3071 (research/centre-block-repair-information, Ross Richardson) and #3097 (research/centre-seven-owner-information-floor, Gonzalo-Mier): Report (author-checked) the ordered route-product uniqueness ($C_4$-freeness), the 50 order-3 braid edges characterizing 6-cycles, and the two-stage 1-to-1 block floors for $|B| \le 6$ (#3071) and $|B| = 7$ (#3097) under merged_for_archive_only and partially_reviewed intake status (building on ywz65's research/centre-owner-observation-floor and Aaron Wang's #2391). Pillar 3 extends that exact framework by establishing the Dependent-Triple Braid Sparsity Theorem (0 of 896 dependent triples in $R$ contain $\ge 2$ braid edges; 846 contain 0 and 50 contain 1), which eliminates all $C_4$-free degree partitions across 7 <= |B| <= 12 and raises the uncharged two-stage 1-to-1 block floor from $|B| \ge 8$ to $|B| \ge 13$.
• Open PR #3120 (research/centre-demand-rank-floor, Aaron Wang / navinor): Reports (author-checked) a demand-rank check and schedule-lookup scan with 16 present / 1,136 missing lookups on S_split = (229..259). Pillar 1 shows that those 1,136 missing lookups arise from keying call["owners"] by global owner ID p[0] on local role indices S_split = (229..259) (which hits only Calls 48 and 64 in Pair 1 of Replica 0), resolves all 1,152 / 1,152 lookups (0 missing) in both split-centres and hosted, and identifies the 96 same-replica shared-data pairs (5 / 5 shared Data Sinks, chronological joint source rank $8$ on $D_{\text{pair}}$).

---

6. Verification & Reproduction Commands

python3.12 -B research/centre-sink-duality-and-braid-quotient/verify.py
python3.12 -B scripts/research_package.py --package research/centre-sink-duality-and-braid-quotient

Expected output:

PASS_CENTRE_SINK_DUALITY_AND_BRAID_QUOTIENT resolved_lookups 1152 same_rep_pairs 96 dep_triples_ge2_braids 0 block_floor_max_B 12 combined_circle_a_cap 0.002367082582 k2_dH8_additive 0.002831949289 k2_dH8_displace 0.003210567561 no_new_kappa

Open next questions

1. Global Compilation of the 16 $(F_0 \to B_1 \to F_2)$ Circle Quotients: Can the 16 same-replica $(F_0 \to B_1 \to F_2)$ circle triples be compiled into a completed global schedule where the 3 intervening stage-0 bridge events and Call 4 (b1) preserve the exact rank_D0_f2 = 0 pre-centre source cancellation and restore the 8 shared accumulator roles across all 16 replicas ($a_{\text{cap}} = 0.002027990479$, or $0.002367082582$ when combined with the Stage-8 zero-feedback circle)?
2. Labelled Braid Incidence Beyond $|B| = 12$: Does any $C_4$-free bipartite incidence graph exist at $|B| \ge 13$ whose 6-cycles are realizable by the 50 order-3 braid edges and their unique dependent-triple extensions in ${77..82}$, or does the two-stage 1-to-1 block-repair obstruction extend all the way to $|B| = 112$?
3. Role-Untangled $k = 2$ Accumulator Transfer Word ($\Delta H \le 31$): Can an explicit accumulator transfer word untangle the 8 local post-$A$ source rows from the 5 Data Sinks (92, 57, 81, 11, 9) and 3 Helper Sinks (224, 240, 256) within the sharp additive break-even budget of $H \le 31$ extra rank-1 operations per call at $T_2$ ($a^* = 0.001733590570$, or $a^* = 0.002831949289$ at $\Delta H = 8$)?

Credit

• Pinned verification inputs (SOURCES.json): Rohan Arun (#1094), Jeremy Kothe, Hao Yan, icekylinx, DreamingOfClouds, Douglas Colkitt, Cinna Davis (1337isnot1337, #1708), Sagar Thakrar (#1012), Ryan Haines, Scratch-net, Chafik Boukhalfa (certificates/selected-result.json and research/community-frontier1094-audit/selected-replay.tar.gz); Douglas Colkitt (research/complex-local-word-ceiling); @ToikY (research/centre-shared-return-guard, #1748).
• Prior centre-sharing formulations, theorems, and open questions built upon here: Aaron Wang / navinor (#2391, #3075 research/centre-shared-kcall-charged-seed615415, open PR #3120 research/centre-demand-rank-floor, and research/selected-centre-quarter-native), ywz65 (research/centre-owner-observation-floor), Ross Richardson (#3071 research/centre-block-repair-information), Gonzalo-Mier (#3097 research/centre-seven-owner-information-floor), rtyu193-rgb (research/centre-sharing-overhead-budget), Sagar Thakrar (#2199, frontier1094-recipes-exact-seed76), Adam Gall (#1918), and commdata2338 (#2048).
• New here (dcharb78, with AI assistance): Pillar 1 (1,152 / 1,152 positional sink decoding across split-centres and hosted gauge44 into 5 Data Sinks + 3 Helper Sinks), Pillar 2 (three exact 704-role forward/backward duality laws and the 10,296-pair Two-Regime Dichotomy identifying the 96 same-replica shared-data pairs), Pillar 3 (Dependent-Triple Braid Sparsity Theorem closing $7 \le |B| \le 12$), Pillar 4 (chronological $(F_0 \to B_1 \to F_2)$ circle cancellation, Stage-8 zero-feedback circle, and 13-row ceiling.ceiling(centre=...) stratification), and the 8 behavioral negative controls in verify.py. Licensed under Apache-2.0.