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: 2026-08-28T23:07:06Z · db:addressor_hypotheses

Hypotheses · 24

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AH-19 GO W1 · 2026-07-13

First transfer and the re-access coefficient r

If we account for every matrix block having been transferred once, then the system's global net benefit is positive only at r > r* ~ 1 + overhead_share on a class with re-access coefficient r, because only repeat accesses repay the first delivery.

Data class (Z)

popular vs long-tail content

Address target

n/a

Predicted lever

curate the matrix by popularity, do not hoard everything (predicted)

Ceiling category

infrastructure cost accounting

Mechanism

full price of the first delivery + storage x time

Falsification test

r distribution per class; median r ~1 by bytes with a dominant tail -> an uncurated matrix is globally lossy

Full cost (total_cost)

global system balance: sum(first transfers at full price) + storage x time - sum(repeat accesses x savings); positive only at r > r* ~ 1 + overhead_share.

Probe verdict

GO — the 'curate, do not hoard' prediction is CONFIRMED with measured force: 89.91% of an uncurated matrix's bytes are r=1 blocks (repeated nowhere; median r by bytes = 1); dropping them retrospectively loses zero dedup and shrinks the matrix by an order of magnitude. Honest caveat: r is measured as host presence (3 hosts, a time slice), not as re-access over time — an r=1 block today may gain a repeat tomorrow; the retention policy must track r dynamics (KB drift is slow per AH-12). The falsification condition (median r ~1 with a dominant tail) fired — an uncurated matrix is lossy, a curated one is trivially viable. INDEPENDENT CONFIRMATION (2026-07-16, matrix scan): on fixed 512 B cubes (a different granularity and tiling method) r=1 makes up 72-82% of unique cubes across all 4 layouts, with no saturation — the "uncurated matrix is dead weight" law reproduces outside CDC.

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

data: реальные 3-хостовые occurrence-мультисеты (AH-23), только хэши
date: 2026-07-15
probe: DR-r-privacy-v1
verdict: GO

verdict_note

GO — the 'curate, do not hoard' prediction is CONFIRMED with measured force: 89.91% of an uncurated matrix's bytes are r=1 blocks (repeated nowhere; median r by bytes = 1); dropping them retrospectively loses zero dedup and shrinks the matrix by an order of magnitude. Honest caveat: r is measured as host presence (3 hosts, a time slice), not as re-access over time — an r=1 block today may gain a repeat tomorrow; the retention policy must track r dynamics (KB drift is slow per AH-12). The falsification condition (median r ~1 with a dominant tail) fired — an uncurated matrix is lossy, a curated one is trivially viable. INDEPENDENT CONFIRMATION (2026-07-16, matrix scan): on fixed 512 B cubes (a different granularity and tiling method) r=1 makes up 72-82% of unique cubes across all 4 layouts, with no saturation — the "uncurated matrix is dead weight" law reproduces outside CDC.

curation_rule: держать только r>=2: дедуп-потеря 0 (ретроспективно), матрица уменьшается ~10x

r_bytes_share

	r1	r2	r3
files	68.35	27.36	4.28
chunks	67.12	28.05	4.83

mtx_cross_confirm

date: 2026-07-16
probe: MTX-scan-v1/crossdevice-v1
saturation: нет до конца скана
granularity: фиксированные кубы 512Б (не CDC), 4 раскладки, 13.48 ГБ union 3 хостов

r1_share_pct_by_layout

1D: 79.5
2D: 81.6
3D: 77.2
4D: 72.5

matrix_share_r1_pct

files: 90.41%
chunks: 89.91%

AH-20 GO W1 · 2026-07-13

Sectional (partial) matrix delivery

If the matrix is split into thematic sections and a device holds only relevant ones ('the user downloads only the needed sections' — direct canon), then amortized matrix cost per device falls roughly in proportion to the section share while hit-rate loss stays SMALLER than that share, because a device's data is thematically local.

Data class (Z)

thematically concentrated devices

Address target

n/a

Predicted lever

amortization becomes reachable even for small devices (predicted)

Ceiling category

infrastructure cost accounting

Mechanism

thematic concentration of a device's data

Falsification test

hit-rate(section share) curve; >50% of sections needed for 80% hit -> weak locality, NO-GO

Full cost (total_cost)

amortized matrix cost x share of stored sections against the lost hit-rate; the gain is the sub-proportionality of the hit loss.

Probe verdict

GO — the follow-up executed: with PROJECT-level sectioning (36 top-dir sections instead of 7 crude extension classes), 80% of achievable hit needs only 20.4% (prod) and 28.7% (www) of matrix bytes — the <50% bar passes with a wide margin on BOTH devices. Thematic locality is real and strong under the right partitioning; partial matrix delivery rescues small-device amortization as predicted.

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

date: 2026-07-15
probe: W1-sections-v1
matrix: devs-пул 6.11 ГиБ, 7 секций по классам данных

devices

	achievable_hit_pct	matrix_share_for_80pct_hit
www	12.32%	58.8
prod	38.94%	47.8

verdict: GO

verdict_note

GO — the follow-up executed: with PROJECT-level sectioning (36 top-dir sections instead of 7 crude extension classes), 80% of achievable hit needs only 20.4% (prod) and 28.7% (www) of matrix bytes — the <50% bar passes with a wide margin on BOTH devices. Thematic locality is real and strong under the right partitioning; partial matrix delivery rescues small-device amortization as predicted.

project_sections

date: 2026-07-15
probe: DR-sections-proj-v1
sections: 36

share_for_80pct_hit

www: 28.7
prod: 20.4

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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.