Pith Number

pith:5PDBHCT3

pith:2012:5PDBHCT3QE5BYSGAQUB3EV3IT2

not attested not anchored not stored refs pending

Symmetric Whitney tower cobordism for bordered 3-manifolds and links

Jae Choon Cha

arxiv:1204.4968 v2 · 2012-04-23 · 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{5PDBHCT3QE5BYSGAQUB3EV3IT2}

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	2026-05-18T03:39:52.991107Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebc6138a7b813a1c48c08503b257689e92efdb24d36388c7863ba4acb9214230

Aliases

arxiv: 1204.4968 · arxiv_version: 1204.4968v2 · doi: 10.48550/arxiv.1204.4968 · pith_short_12: 5PDBHCT3QE5B · pith_short_16: 5PDBHCT3QE5BYSGA · pith_short_8: 5PDBHCT3

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/5PDBHCT3QE5BYSGAQUB3EV3IT2 \
  | 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: ebc6138a7b813a1c48c08503b257689e92efdb24d36388c7863ba4acb9214230

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f47f81fd3e4dd58c1a199840af1161284a1201f9b6a22453b076e07fcd9cfac9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-04-23T04:15:49Z",
    "title_canon_sha256": "a51e9e46261e9d4a43b5193d80284e12eac68f1fe52677f3e09fb560d9e15443"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.4968",
    "kind": "arxiv",
    "version": 2
  }
}