Pith Number

pith:ECDWIBYP

pith:2019:ECDWIBYPJIV5BSLGG2J5A44GDK

not attested not anchored not stored refs pending

On defining products of cobordism classes of Morse functions

Naoki Kitazawa

arxiv:1902.04101 v2 · 2019-02-11 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ECDWIBYPJIV5BSLGG2J5A44GDK}

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	2026-05-17T23:51:04.986160Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

208764070f4a2bd0c9663693d073861ab07c9e6d167a15959548dde94e041e82

Aliases

arxiv: 1902.04101 · arxiv_version: 1902.04101v2 · doi: 10.48550/arxiv.1902.04101 · pith_short_12: ECDWIBYPJIV5 · pith_short_16: ECDWIBYPJIV5BSLG · pith_short_8: ECDWIBYP

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/ECDWIBYPJIV5BSLGG2J5A44GDK \
  | 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: 208764070f4a2bd0c9663693d073861ab07c9e6d167a15959548dde94e041e82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84e1f3be68c85001f75589b97fc74d473b018dd4a78fa7336cc4341a0ac73e0b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2019-02-11T19:16:05Z",
    "title_canon_sha256": "486e5f64a38b76cd16e6a5959f3e0140b5832b3e6def2825e7bc7a676f39b17e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.04101",
    "kind": "arxiv",
    "version": 2
  }
}