Pith Number

pith:4ECQC54M

pith:2026:4ECQC54MDC5OWPYH6TFC2327A7

not attested not anchored not stored refs pending

Expressivity of congruence-based architectures for DNNs on positive-definite matrices

Antonin Oswald, Estelle Massart

arxiv:2606.02490 v1 · 2026-06-01 · cs.LG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4ECQC54MDC5OWPYH6TFC2327A7}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-06-02T03:05:07.654693Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e10501778c18baeb3f07f4ca2d6f5f07cac00e393201bc43ccd26393bc3496b5

Aliases

arxiv: 2606.02490 · arxiv_version: 2606.02490v1 · doi: 10.48550/arxiv.2606.02490 · pith_short_12: 4ECQC54MDC5O · pith_short_16: 4ECQC54MDC5OWPYH · pith_short_8: 4ECQC54M

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4ECQC54MDC5OWPYH6TFC2327A7 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: e10501778c18baeb3f07f4ca2d6f5f07cac00e393201bc43ccd26393bc3496b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aff58b3697b6b805f272ab94686d857f4d24c04ab65f9407af0c0487a59bb3ae",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-01T17:01:08Z",
    "title_canon_sha256": "ec6d7831ce40f9a7864eb2e9fcf7d1fbe69585033e143bb55a91f1320f4e5982"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.02490",
    "kind": "arxiv",
    "version": 1
  }
}