Pith Number

pith:PLRR4TXP

pith:2010:PLRR4TXPIWSWWTMK3VWWZQABO4

not attested not anchored not stored refs pending

Symplectic homology product via Legendrian surgery

Frederic Bourgeois, Tobias Ekholm, Yakov Eliashberg

arxiv:1012.4218 v4 · 2010-12-19 · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PLRR4TXPIWSWWTMK3VWWZQABO4}

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	2026-05-18T01:11:13.951502Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ae31e4eef45a56b4d8add6d6cc0017703d1400b7fc84771e5505dcdf6ddbd89

Aliases

arxiv: 1012.4218 · arxiv_version: 1012.4218v4 · doi: 10.48550/arxiv.1012.4218 · pith_short_12: PLRR4TXPIWSW · pith_short_16: PLRR4TXPIWSWWTMK · pith_short_8: PLRR4TXP

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/PLRR4TXPIWSWWTMK3VWWZQABO4 \
  | 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: 7ae31e4eef45a56b4d8add6d6cc0017703d1400b7fc84771e5505dcdf6ddbd89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2bcab912a5ce40f1f137f7e765d67b64c7c971953e530abd0843e45ad0f7340",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2010-12-19T23:26:07Z",
    "title_canon_sha256": "66b5707d627e752a9efe09025196cf2c33dacd599067f3fbed9832f4cb95b085"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4218",
    "kind": "arxiv",
    "version": 4
  }
}