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: 2026-08-28T23:15:22Z · db:addressor_hypotheses

Hypotheses · 24

Page 4 / 12

AH-07 NO-GO W1 · 2026-07-13

Two-level fragment address into the matrix

If a fragment address is (version, section, offset, len, flags) ~16-24 B for a fragment already present in the matrix, then net bytes on structured boilerplate drop by covered_fraction x (1 - address/fragment_len), because typical fragments are long and frequent.

Data class (Z)

boilerplate, licenses, templates, format wrappers, copy-pasted code

Address target

24 B

Predicted lever

coverage by fragments >=256 B on office/code/web classes 20-60% (prediction)

Ceiling category

shared context (dictionary / fragments)

Mechanism

a reference is cheaper than a long frequent fragment

Falsification test

corpus scan: coverage <15% OR savings <= zstd-with-dictionary -> NO-GO (AH-01 subsumes)

Full cost (total_cost)

address: 16-24 B x fragment count · metadata: insertion-point markup (its own decoder branch — charged per Gotcha #6) · residual: uncovered bytes through the local codec · amortized: matrix sections holding the fragment pool.

Probe verdict

NO-GO — both pre-registered conditions fired: coverage by >=256 B fragments is only 10.69% (<15%) AND savings <= the zstd dictionary (per-file: fragments 0.2781 without catalog / 0.3017 with catalog vs dictionary 0.2664). The first probe version showed an apparent win — the AH-22 stand caught the confound (the residual was compressed as one solid stream against per-file baselines); with arms aligned the win vanished: the solid scenario with the catalog charged is 0.228 vs solid local 0.2153. Fragment addressing on this class degenerates into what a dictionary provides more cheaply.

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

date: 2026-07-14
probe: W1-fragments-v1b-fair

solid

L0_solid: 0.2153
A_no_catalog: 0.2044
A_with_catalog: 0.228

class_z

small structured files (<128 KiB, text-ish), real KB

verdict: NO-GO

per_file

L1_dict: 0.2664
A_no_catalog: 0.2781
A_with_catalog: 0.3017

coverage_pct: 10.69%

verdict_note

NO-GO — both pre-registered conditions fired: coverage by >=256 B fragments is only 10.69% (<15%) AND savings <= the zstd dictionary (per-file: fragments 0.2781 without catalog / 0.3017 with catalog vs dictionary 0.2664). The first probe version showed an apparent win — the AH-22 stand caught the confound (the residual was compressed as one solid stream against per-file baselines); with arms aligned the win vanished: the solid scenario with the catalog charged is 0.228 vs solid local 0.2153. Fragment addressing on this class degenerates into what a dictionary provides more cheaply.

pool_fragments: 221 086

AH-08 GO W1 · 2026-07-13

Entropy coding of the reference stream

If the stream of matrix references is rANS-coded (frequent fragments get short codes), then the average reference cost on Zipf-distributed access classes falls from a nominal 16-32 B to effective single bytes, because access to a shared matrix is heavily skewed toward top fragments.

Data class (Z)

anything with Zipf-like access (web/code)

Address target

n/a

Predicted lever

top 1% of fragments >=50% of accesses (prediction)

Ceiling category

shared context (dictionary / fragments)

Mechanism

skewed reference distribution -> short codes for frequent entries

Falsification test

access distribution on a web/code corpus; near-uniform -> no lever; charge through the real backend (Gotcha #11)

Full cost (total_cost)

address: compressed by rANS down to the entropy of the access distribution · metadata: coder frequency tables/context · residual: unchanged · amortized: unchanged.

Probe verdict

GO with a mechanism correction: the metric is CONFIRMED (2.15 B/ref vs the 32 B nominal, −93.28% on a real stream of 325,048 references), but the predicted mechanism is REFUTED — there is no Zipf skew (the top 1% of catalog entries carries only 8.83% of accesses, not >=50%). The real source of the win is the ordinal into the shared catalog (~log2(633,603)=19.3 bits for a first reference) plus adaptive repeat codes, with no side tables (both ends learn from the shared stream — Gotcha #9/#11 discipline). Engineering takeaway: code references as ordinals + adaptively; do not count on skew. MULTI-CLASS (2026-07-15): the effective reference cost is stable across all 7 classes — 1.32-2.17 B (the ordinal+adaptive mechanism is class-independent).

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

date: 2026-07-15
probe: W1-zipf-v1
stream: реальный поток chunk-hit ссылок (тот же обход, что W1-router-v1)
verdict: GO

multiclass

date: 2026-07-15
probe: DR-multiclass-v1

eff_bytes_per_ref_by_class

web: 1.32
code: 2.02
docs: 1.81
media: 2.17
other: 2.09
config: 1.65
archives: 1.51

refs_total: 325 048

verdict_note

GO with a mechanism correction: the metric is CONFIRMED (2.15 B/ref vs the 32 B nominal, −93.28% on a real stream of 325,048 references), but the predicted mechanism is REFUTED — there is no Zipf skew (the top 1% of catalog entries carries only 8.83% of accesses, not >=50%). The real source of the win is the ordinal into the shared catalog (~log2(633,603)=19.3 bits for a first reference) plus adaptive repeat codes, with no side tables (both ends learn from the shared stream — Gotcha #9/#11 discipline). Engineering takeaway: code references as ordinals + adaptively; do not count on skew. MULTI-CLASS (2026-07-15): the effective reference cost is stable across all 7 classes — 1.32-2.17 B (the ordinal+adaptive mechanism is class-independent).

catalog_entries: 633 603
nominal_ref_bytes: 9.92 MiB (10 401 536 B)
top1pct_share_pct: 8.83%
adaptive_ref_bytes: 683.01 KiB (699 398 B)
distinct_over_refs: 0.4618
referenced_entries: 150 098
saving_vs_nominal_pct: 93.28%
effective_bytes_per_ref: 2.15

Page 4 / 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.