Pith Number

pith:Z6IJBPJE

pith:2012:Z6IJBPJEUO63PH7TABFH6DBG5F

not attested not anchored not stored refs pending

Link invariants via counting surfaces

Michael Brandenbursky

arxiv:1209.0420 v2 · 2012-09-03 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z6IJBPJEUO63PH7TABFH6DBG5F}

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	2026-05-18T00:56:52.518668Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf9090bd24a3bdb79ff3004a7f0c26e951eb7efde090672bd3635d5e9662d847

Aliases

arxiv: 1209.0420 · arxiv_version: 1209.0420v2 · doi: 10.48550/arxiv.1209.0420 · pith_short_12: Z6IJBPJEUO63 · pith_short_16: Z6IJBPJEUO63PH7T · pith_short_8: Z6IJBPJE

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/Z6IJBPJEUO63PH7TABFH6DBG5F \
  | 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: cf9090bd24a3bdb79ff3004a7f0c26e951eb7efde090672bd3635d5e9662d847

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee1e8899277636ef6bd6a12a677d4bcc2947eec03a39807eff805318c49d3d02",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-09-03T18:03:06Z",
    "title_canon_sha256": "b583af7c638159cf895e305c9ad60d78fd0e4fb3079f71c966109e9da314462f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0420",
    "kind": "arxiv",
    "version": 2
  }
}