Pith Number

pith:6L4SLTJW

pith:2010:6L4SLTJWEUPEF4MAGYP7D2TRCE

not attested not anchored not stored refs pending

Divergences on projective modules and non-commutative integrals

Tomasz Brzezi\'nski

arxiv:1010.1470 v2 · 2010-10-07 · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6L4SLTJWEUPEF4MAGYP7D2TRCE}

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	2026-05-18T04:17:15.192683Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f2f925cd36251e42f180361ff1ea7111328335ddd40524ecd4ea77be5189ea7f

Aliases

arxiv: 1010.1470 · arxiv_version: 1010.1470v2 · doi: 10.48550/arxiv.1010.1470 · pith_short_12: 6L4SLTJWEUPE · pith_short_16: 6L4SLTJWEUPEF4MA · pith_short_8: 6L4SLTJW

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/6L4SLTJWEUPEF4MAGYP7D2TRCE \
  | 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: f2f925cd36251e42f180361ff1ea7111328335ddd40524ecd4ea77be5189ea7f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2147dc68fbe292a09179fb11b3984e91426f68d5eff63cabf1e90eb6709c9ff",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2010-10-07T16:13:51Z",
    "title_canon_sha256": "3fd2637e07b346ad7878b3113e4300910b90a6f794166333149db94c126abe2d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.1470",
    "kind": "arxiv",
    "version": 2
  }
}