Pith Number

pith:XPUB54RM

pith:2011:XPUB54RM2CBK3GZTVQTLXOCQW2

not attested not anchored not stored refs pending

Geometric Poincar\'e Lemma

Jenny Harrison

arxiv:1101.0313 v2 · 2011-01-01 · math.AT · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XPUB54RM2CBK3GZTVQTLXOCQW2}

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.

Cited by

1 paper in Pith

The Poincare lemma, antiexact forms, and fermionic quantum harmonic oscillator

Receipt and verification

First computed	2026-05-18T02:23:05.864436Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bbe81ef22cd082ad9b33ac26bbb850b6b8b21394d880ddf7784ab605f21b9836

Aliases

arxiv: 1101.0313 · arxiv_version: 1101.0313v2 · doi: 10.48550/arxiv.1101.0313 · pith_short_12: XPUB54RM2CBK · pith_short_16: XPUB54RM2CBK3GZT · pith_short_8: XPUB54RM

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/XPUB54RM2CBK3GZTVQTLXOCQW2 \
  | 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: bbe81ef22cd082ad9b33ac26bbb850b6b8b21394d880ddf7784ab605f21b9836

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0baf3154a826206c331da56d142b93bf9d7af083e82eb90f55499c0dbc5708ed",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2011-01-01T02:06:25Z",
    "title_canon_sha256": "439e26b207e89ed1a22f80c11b2886ff16874724dec56975052efef6506d757b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.0313",
    "kind": "arxiv",
    "version": 2
  }
}