Cubrim — Global Addresser

The honest limit, stated first

A fixed short code can distinguish only a finite number of states, while the space of possible files grows exponentially with length — so a short address alone can never uniquely denote every long sequence. An address is meaningful only together with a catalog where the object already exists. And any honest result must charge the full cost: the addresses, the metadata, the residual data — and the shared matrix itself, which is only worth its size when amortized across many files and devices. Cubrim-2 therefore does not promise to “compress any file into 16 bytes”. It maps where global addressing genuinely beats local compression — and records, just as openly, where it structurally cannot.

How much space would ALL possible matrices take

We count in bits. An N-dimensional cube is a visual arrangement of a bit sequence: a 4×4×4 cube is 64 bits laid out in three dimensions. Dimensionality (1D/2D/3D/4D) is a way to arrange the same bits, not a different amount of them. Hence the number of all possible matrices of length B bits is 2^B and depends only on B: a 64-bit 1D string and a 4×4×4 cube share the same 2^64 ≈ 1.8×10^19 states.

B, bits	cube example	all possible = 2^B	store them all (bytes)	fits in 20,000×1 TB?
8	2×2×2	2.56×10²	2.56×10² B	yes
27	3×3×3	1.34×10⁸	4.53×10⁸ B	yes
51	—(порог/threshold)	2.25×10¹⁵	1.44×10¹⁶ B	yes
64	4×4×4	1.84×10¹⁹	1.48×10²⁰ B	no
125	5×5×5	4.25×10³⁷	6.65×10³⁸ B	no
256	4×4×4×4 (4D)	1.16×10⁷⁷	3.71×10⁷⁸ B	no
1000	10×10×10	1.07×10³⁰¹	1.34×10³⁰³ B	no
4096	8×8×8×8 (4D)	1.04×10¹²³³	5.35×10¹²³⁵ B	no

Capacity yardstick: 20,000 disks of 1 TB = 2×10^16 bytes = 1.6×10^17 bits. The full-enumeration threshold is B = 51 bits: the last length at which all 2^B matrices (with their contents, 2^B×B bits = 1.44×10^16 bytes) still fit; at B = 52 they no longer do (2.93×10^16 bytes). A 4×4×4 cube (64 bits): just the 64-bit addresses of all 2^64 matrices would take 1.48×10^20 bytes ≈ 147.6 EB — four orders of magnitude beyond the yardstick. At B = 256 there are 1.16×10^77 matrices — still slightly fewer than the atoms in the observable universe (~10^80); the “more than atoms” line is crossed at B ≈ 266. Beyond that, super-exponential growth with no physical storage prospect whatsoever.

The honest conclusion: “all possible matrices” cannot be enumerated — 2^B diverges super-exponentially at lengths below a single machine word. So the Addresser stores not all possible blocks but only the ones ACTUALLY ENCOUNTERED (CAS/deduplication): their number is bounded by the volume of real data and obeys the track’s measured laws — 89.9% of blocks in an uncurated matrix occur exactly once (AH-19), and an honest 16–64 bytes per object is achievable only on an exact match against the catalog (AH-05). This is the same fundamental limit as the block above: an address is meaningful only together with a catalog where the object already exists.

On dimensionality: 2^B does not depend on it, but dimensionality changes which bits land in one cube when REAL data is tiled — and therefore how many unique cubes occur in practice. That is measured by a scan (part B of the experiment), not by a formula.

Formulas: number of matrices = 2^B; storing the contents = 2^B × B bits; the ordinal address of one matrix = B bits (2^B states). All numbers are computed with exact integer arithmetic (python), not estimates.

How much space the ACTUALLY encountered matrices need (scan experiment)

A real CROSS-DEVICE corpus of 13.48 GB (a union of three hosts: arcana-devs 9.06 + arcana-www 3.38 + arcana-prod 1.04 GB; the hosts exchanged only cube hashes) was tiled into cubes of B = 4096 bits (512 bytes) in four layouts of the same length: a 1D string of 4096, 2D 64×64, 3D 16×16×16, 4D 8×8×8×8. A layout groups DIFFERENT bits of the file into one cube (strided tiling with a 4096-byte row), so the number of unique cubes on real data differs — even though the number of possible ones (2^4096) is identical.

layout	cubes scanned	unique	% unique	cross-host overlap (cubes)	store the unique
1D 4096	25 890 520	14 965 607	57.80%	1 847 617	7.14 GiB
2D 64×64	19 368 448	12 077 059	62.35%	1 260 924	5.76 GiB
3D 16×16×16	13 959 168	8 020 728	57.46%	943 354	3.82 GiB
4D 8×8×8×8	10 518 528	5 578 363	53.03%	768 085	2.66 GiB

There is NO saturation: the number of unique cubes grows almost linearly to the very end of the scan (devs-slice curve: 1D 10.9M unique at 7.3 GB → 12.3M at 8.3 GB) — real data at this cube length hardly “runs out”. On the devs slice, 72–82% of unique cubes were seen exactly once — the same measured law as AH-19 (89.9% on CDC chunks): an uncurated matrix is mostly dead weight. Cross-host overlap is real (0.77–1.85M cubes are shared between hosts), and it is what lowers the union corpus unique share to 53–62%.

Disks for the scan itself: 2.7–7.1 GiB of unique matrices per 13.48 GB of cross-device data — a fraction of one 1 TB disk. Extrapolating to the world’s stored data (on the order of 10 ZB = 10^22 bytes; order-of-magnitude per IDC Global DataSphere reports): with the measured 53–62% unique share on the cross-device corpus and NO saturation, the matrices would take ~5.3–6.2 ZB — billions of 1 TB disks, i.e. the same order as the data itself. THE EXTRAPOLATION IS LINEAR AND MARKED AS AN ASSUMPTION: the world corpus differs in composition, and saturation at larger volumes is not excluded — it was simply not observed in the scan.

Conclusions: (1) even storing only the ENCOUNTERED matrices at world scale is the same order as the data itself — the Addresser’s win lives not in a “warehouse of all cubes” but in deduplicating the repeated share (38–47% on the union corpus) and in r≥2 curation (AH-19); (2) the optimal layout by the “fewer unique” criterion is 4D (53.0% unique vs 62.4% for 2D on the union corpus) — multidimensional grouping does gather repeating bits more often, with a moderate margin (~6–9 pp); (3) the comparison is honest with a caveat: layouts need different alignment (2D — 256 KB blocks, 4D — 2 MB), so corpus coverage differs — figures are per each layout’s covered share.

Scripts: probe_matrix_scan.py + matrix_scan_dump.py (strides in the header; the cross-device union exchanges hashes only, MTX-scan-crossdevice-v1); cube hash blake2b-96; saturation curve checkpointed every 500 MB; all figures measured, the extrapolation labeled.

Wave 1 — research complete

Wave-1 deep research is complete: each of the 24 hypotheses carries a real measured verdict (full-cost charged accounting, falsification test executed, script+SHA on the card). GO means the mechanism works and is measured; NO-GO means it is closed by measurement or strict arithmetic. Predicted levers remain predictions and are labeled; the measured numbers live in every card below.

NO-GO · 9 GO · 15

shared context (dictionary / fragments) · 4 identity dedup — reference ≪ payload on exact match · 3 structurally cannot win (boundary) · 4 infrastructure cost accounting · 10 near-match + delta · 3

Generated: 2026-08-29T00:16:17Z · db:addressor_hypotheses

Hypotheses · 24

Page 6 / 12

AH-11 GO W1 · 2026-07-13

Break-even threshold N*

If the benefit is formalized as B(N) = sum(savings) - M_size - C_catalog_sync - C_residual_overhead, then a measurable threshold N* exists, reachable on enterprise-backup classes and N* -> infinity on unique personal content, because savings are proportional to cross-device repetition.

Data class (Z)

enterprise backup vs personal-unique

Address target

n/a

Predicted lever

the formula plus an N* table per class — the track's honesty gauge

Ceiling category

infrastructure cost accounting

Mechanism

amortizing the matrix's fixed cost through repetition

Falsification test

compute N* on 2-3 real mixes; classes with N* beyond a realistic fleet are 'outside the Addresser's market'

Full cost (total_cost)

this IS the track's total_cost aggregator: B(N) = sum(savings(N)) - M_size - C_catalog_sync(N) - C_residual_overhead(N); threshold N* = root of B.

Probe verdict

GO — both predictions confirmed on MEASURED parameters: for the office/infra class the break-even threshold exists and is tiny (N*=2: the second device already turns the balance positive, +0.613 GiB), for the unique personal class c~0 -> N* -> infinity (a clean personal corpus is the AH-16 follow-up). The formula and N* table are the track's honesty gauge; matrix distribution equals the devices' own data acquisition (first transfers charged under AH-19). MULTI-CLASS (2026-07-15): N*=2 is UNIVERSAL across all 7 measured classes (even media at a 6.9% cross rate); N*->infinity remains only for the measurement-verified unique class (AH-16).

Measured result (raw research log; descriptors partly in the RU original)

date: 2026-07-14

B_GiB

N1: -0.019
N2: 0.613
N3: 1.245
N10: 5.669
N100: 62.555

probe: W1-nstar-v1
formula: B(N) = c*d*(N-1) - 2*k_cat*u*N
verdict: GO

multiclass

date: 2026-07-15

note

кросс-ставки классов 5.8–27.6% при k_cat=0.00419 дают N*=2 везде

probe: DR-multiclass-v1

nstar_by_class

web: 2
code: 2
docs: 2
media: 2
other: 2
config: 2
archives: 2

verdict_note

GO — both predictions confirmed on MEASURED parameters: for the office/infra class the break-even threshold exists and is tiny (N*=2: the second device already turns the balance positive, +0.613 GiB), for the unique personal class c~0 -> N* -> infinity (a clean personal corpus is the AH-16 follow-up). The formula and N* table are the track's honesty gauge; matrix distribution equals the devices' own data acquisition (first transfers charged under AH-19). MULTI-CLASS (2026-07-15): N*=2 is UNIVERSAL across all 7 measured classes (even media at a 6.9% cross rate); N*->infinity remains only for the measurement-verified unique class (AH-16).

inputs_measured

source: W1-crossdevice-v1 (3 реальных хоста) + AH-09 catalog-модель
c_cross_chunk_dup: 0.1621
d_bytes_per_device: 4 313 821 344
u_unique_per_device: 2 458 446 783
k_cat_per_unique_byte: 0.00419

N_star_office_infra: 2

AH-12 GO W1 · 2026-07-13

Frozen-matrix drift

If the matrix is frozen (immutable v1, as the canon requires), then hit-rate on fresh content degrades monotonically at a measurable d(hit)/dt, because real data distributions are non-stationary while a frozen matrix is a snapshot of the past.

Data class (Z)

news, updating software, new formats

Address target

n/a

Predicted lever

dictionary sections decay faster than chunk sections (prediction, no numbers)

Ceiling category

infrastructure cost accounting

Mechanism

data non-stationarity vs a snapshot of the past

Falsification test

hit-rate(t) on dated corpus snapshots

Full cost (total_cost)

each new matrix version costs distribution+sync per device; the gain is the recovered hit-rate; the net effect is the difference.

Probe verdict

GO — monotonic decay of a frozen matrix is MEASURED on real dated KB snapshots: 100 -> 98.58 -> 97.37 -> 96.86% over 2.5 months, d(hit)/dt ~ −1.3 pp/month. For the KB class the drift is slow, so the matrix version cadence can be low (quarterly), with each version's cost remaining a total_cost line item. Window limits stated honestly: 2.5 months, one class (KB), chunk sections only (deeper git history unavailable — the ecosystem reset of 2026-05-11); dictionary-vs-chunk section comparison is a follow-up. MULTI-CLASS (2026-07-15): the -1.3 pp/month aggregate hid an order-of-magnitude spread — media 100% stable, other 98.2%, config 82.4%, code 74.6%, docs 28.6% over 2.5 months; the matrix version cadence must be PER-CLASS (media: almost never, docs: weeks). DICTIONARY SECTION (2026-07-16): the sub-prediction that dictionary sections drift faster than chunk sections is REFUTED — the frozen dictionary gain did not fall but slightly grew (5.02 -> 6.03 pp over 2.5 months): boilerplate statistics stay stable while exact docs chunks decay to 28.6%. Statistical matrix sections age SLOWER than exact-match ones.

Measured result (raw research log; descriptors partly in the RU original)

date: 2026-07-15
probe: W1-drift-v1
matrix: замороженный чанк-пул KB-снапшота 2026-05-01 (git 4101a640), 32317 чанков
method: git ls-tree/cat-file датированных коммитов (read-only, без checkout), blob-oid кэш
verdict: GO

hit_curve

#1

date: 2026-05-01
hit_pct: 100%

#2

date: 2026-06-01
hit_pct: 98.58%

#3

date: 2026-07-01
hit_pct: 97.37%

#4

date: 2026-07-15
hit_pct: 96.86%

dict_drift

date: 2026-07-16
dict: 110КиБ zstd-19, обучен на снапшоте 2026-05-01 (docs/code/config блобы)
probe: DR-dict-drift-v1

gain_pp_by_date

2026-05-01: 5.02
2026-06-01: 5.67
2026-07-01: 5.95
2026-07-16: 6.03

verdict_note

GO — monotonic decay of a frozen matrix is MEASURED on real dated KB snapshots: 100 -> 98.58 -> 97.37 -> 96.86% over 2.5 months, d(hit)/dt ~ −1.3 pp/month. For the KB class the drift is slow, so the matrix version cadence can be low (quarterly), with each version's cost remaining a total_cost line item. Window limits stated honestly: 2.5 months, one class (KB), chunk sections only (deeper git history unavailable — the ecosystem reset of 2026-05-11); dictionary-vs-chunk section comparison is a follow-up. MULTI-CLASS (2026-07-15): the -1.3 pp/month aggregate hid an order-of-magnitude spread — media 100% stable, other 98.2%, config 82.4%, code 74.6%, docs 28.6% over 2.5 months; the matrix version cadence must be PER-CLASS (media: almost never, docs: weeks). DICTIONARY SECTION (2026-07-16): the sub-prediction that dictionary sections drift faster than chunk sections is REFUTED — the frozen dictionary gain did not fall but slightly grew (5.02 -> 6.03 pp over 2.5 months): boilerplate statistics stay stable while exact docs chunks decay to 28.6%. Statistical matrix sections age SLOWER than exact-match ones.

multiclass_drift

date: 2026-07-15
probe: DR-drift-class-v1 sha:72e42ecf

hit_pct_at_2026-07-15_vs_frozen_2026-05-01

code: 74.55
docs: 28.6
media: 100
other: 98.24
config: 82.39

drift_pp_per_month: 1.3

Page 6 / 12

Where the Addresser cannot beat local compression

Six boundaries are fixed by wave 1 as explicit anti-hypotheses and no-win zones: unique high-entropy data (personal media, encrypted streams — nothing repeats globally); tiny unique files below the inversion point (fixed catalog costs exceed any saving); mathematically generated matrices (an address into an exhaustive or random pool costs at least as much as the content itself); a byte histogram or hash used as the data carrier (order is lost and buying it back costs the file’s entropy); long-tail content fetched roughly once (the first transfer is never repaid); and fragment schemes whose gain collapses into what a shared dictionary already provides. A tiny fixed-size reference per object (tens of bytes) is honestly achievable only on an exact match against a catalog that already stores the object; everywhere else the win criterion is simply that the reference plus all charged costs stay well below the payload it replaces — the reference size is a metric to minimize, not a hard gate.