Pith Number

pith:XQZA5GJM

pith:2013:XQZA5GJMKYEDXM7SEG22NTNG47

not attested not anchored not stored refs pending

Lips and swallow-tails of singularities of product maps

Kazuto Takao

arxiv:1305.1168 v4 · 2013-05-06 · 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{XQZA5GJMKYEDXM7SEG22NTNG47}

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	2026-05-18T02:30:40.636799Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc320e992c56083bb3f221b5a6cda6e7fbbe3de1c7a13aee0cfaf8bf95188ff4

Aliases

arxiv: 1305.1168 · arxiv_version: 1305.1168v4 · doi: 10.48550/arxiv.1305.1168 · pith_short_12: XQZA5GJMKYED · pith_short_16: XQZA5GJMKYEDXM7S · pith_short_8: XQZA5GJM

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/XQZA5GJMKYEDXM7SEG22NTNG47 \
  | 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: bc320e992c56083bb3f221b5a6cda6e7fbbe3de1c7a13aee0cfaf8bf95188ff4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19a5bd8f2a15e516dd5df8ca6bfe0455c379b06bf727609e5f7804ab9e782ad0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-05-06T12:47:26Z",
    "title_canon_sha256": "e9ce3d57356cb484808b2794d9bda69112b739428cce6a0884da079389d52d15"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.1168",
    "kind": "arxiv",
    "version": 4
  }
}