Pith Number

pith:VV3UBJYE

pith:2025:VV3UBJYEM6QNAH4GZOMPVILIGD

not attested not anchored not stored refs pending

A trace pairing and Elliott invariant for groupoid homology

Robin Deeley, Rufus Willett

arxiv:2509.03759 v1 · 2025-09-03 · math.OA · math.AT · math.DS · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VV3UBJYEM6QNAH4GZOMPVILIGD}

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	2026-07-05T12:04:45.478986Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad7740a70467a0d01f86cb98faa16830e8b647e293e557629b9b3cd648c09af7

Aliases

arxiv: 2509.03759 · arxiv_version: 2509.03759v1 · doi: 10.48550/arxiv.2509.03759 · pith_short_12: VV3UBJYEM6QN · pith_short_16: VV3UBJYEM6QNAH4G · pith_short_8: VV3UBJYE

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/VV3UBJYEM6QNAH4GZOMPVILIGD \
  | 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: ad7740a70467a0d01f86cb98faa16830e8b647e293e557629b9b3cd648c09af7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "943dc9fd6af000c294d8f7d2c19dceca2bf407402f3b0f5e70b2f73832e3f749",
    "cross_cats_sorted": [
      "math.AT",
      "math.DS",
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2025-09-03T22:58:31Z",
    "title_canon_sha256": "6027f27b33c5b3df99506cedc78f20c29314ac92a47edbb1c90acc5a23cb1fb3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.03759",
    "kind": "arxiv",
    "version": 1
  }
}