Pith Number

pith:KHR6OFD7

pith:2012:KHR6OFD7J7HZXTUNTL2VTBHPD5

not attested not anchored not stored refs pending

Morse theory for manifolds with boundary

Andr\'as N\'emethi, Andrew Ranicki, Maciej Borodzik

arxiv:1207.3066 v4 · 2012-07-12 · math.GT · 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{KHR6OFD7J7HZXTUNTL2VTBHPD5}

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	2026-05-18T01:15:47.357254Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51e3e7147f4fcf9bce8d9af55984ef1f6ec41ba52842652229f65d099f784430

Aliases

arxiv: 1207.3066 · arxiv_version: 1207.3066v4 · doi: 10.48550/arxiv.1207.3066 · pith_short_12: KHR6OFD7J7HZ · pith_short_16: KHR6OFD7J7HZXTUN · pith_short_8: KHR6OFD7

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/KHR6OFD7J7HZXTUNTL2VTBHPD5 \
  | 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: 51e3e7147f4fcf9bce8d9af55984ef1f6ec41ba52842652229f65d099f784430

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a37894823a65512b3a03b4b7ce7377e11f8be637d28cda32de6ccfc8d7c2fa3c",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-07-12T19:09:43Z",
    "title_canon_sha256": "95823b76788258f2adba36037de52e91b865bd63ae2f71ed1c15a7342aa07763"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.3066",
    "kind": "arxiv",
    "version": 4
  }
}