Pith Number

pith:MLTLPS55

pith:2013:MLTLPS5543DBOJDRAR3TB7U7PT

not attested not anchored not stored refs pending

A proof of Morse's theorem about the cancellation of critical points

Francois Laudenbach (LMJL)

arxiv:1307.2545 v1 · 2013-07-09 · 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{MLTLPS5543DBOJDRAR3TB7U7PT}

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	2026-05-18T03:18:52.223970Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62e6b7cbbde6c6172471047730fe9f7cd61620be7fa090bcd1ecd0027d4dc2b8

Aliases

arxiv: 1307.2545 · arxiv_version: 1307.2545v1 · doi: 10.48550/arxiv.1307.2545 · pith_short_12: MLTLPS5543DB · pith_short_16: MLTLPS5543DBOJDR · pith_short_8: MLTLPS55

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/MLTLPS5543DBOJDRAR3TB7U7PT \
  | 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: 62e6b7cbbde6c6172471047730fe9f7cd61620be7fa090bcd1ecd0027d4dc2b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c05669bf74afe76dc245d51b9ab8b0952d23a4d7d4ea670ad076c5de03475cb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-07-09T19:21:56Z",
    "title_canon_sha256": "6f6d7482b7f9f2e3662296394ed8a6aaf9298a991bcc7e7161dc0017b7bdbbc5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.2545",
    "kind": "arxiv",
    "version": 1
  }
}