Pith Number

pith:PVFTOH3A

pith:2008:PVFTOH3AMRJNFQOIOQE7SYXSKK

not attested not anchored not stored refs pending

Birth and death in discrete Morse theory

Henry King, Kevin Knudson, Neza Mramor

arxiv:0808.0051 v4 · 2008-08-01 · math.AT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PVFTOH3AMRJNFQOIOQE7SYXSKK}

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	2026-05-18T01:19:14.786948Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d4b371f606452d2c1c87409f962f252a3e461be8e31f7edddc59c1b67eecb73

Aliases

arxiv: 0808.0051 · arxiv_version: 0808.0051v4 · doi: 10.48550/arxiv.0808.0051 · pith_short_12: PVFTOH3AMRJN · pith_short_16: PVFTOH3AMRJNFQOI · pith_short_8: PVFTOH3A

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/PVFTOH3AMRJNFQOIOQE7SYXSKK \
  | 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: 7d4b371f606452d2c1c87409f962f252a3e461be8e31f7edddc59c1b67eecb73

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f2d4e28cd7ef3e5b5c3b07a722ca019a87bee152411b912f65e8a961f3646391",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2008-08-01T02:38:13Z",
    "title_canon_sha256": "bd25fed60a1ea9be75aebe0177b10a030ad23aaa4de2c7d85f5efc1764f74b9f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0808.0051",
    "kind": "arxiv",
    "version": 4
  }
}