Pith Number

pith:P5E5IMBK

pith:2007:P5E5IMBKG5TPVOLDGUT35KJAPJ

not attested not anchored not stored refs pending

Quantifying Homology Classes II: Localization and Stability

Chao Chen, Daniel Freedman

arxiv:0709.2512 v2 · 2007-09-16 · cs.CG · cs.CC · 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{P5E5IMBKG5TPVOLDGUT35KJAPJ}

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	2026-05-18T04:09:14.511851Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f49d4302a3766fab9633527bea9207a651148c2733d063d1da02b31b2caa8a0

Aliases

arxiv: 0709.2512 · arxiv_version: 0709.2512v2 · doi: 10.48550/arxiv.0709.2512 · pith_short_12: P5E5IMBKG5TP · pith_short_16: P5E5IMBKG5TPVOLD · pith_short_8: P5E5IMBK

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/P5E5IMBKG5TPVOLDGUT35KJAPJ \
  | 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: 7f49d4302a3766fab9633527bea9207a651148c2733d063d1da02b31b2caa8a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "76712f5e9cd7657afb7140abd30864d8cfc1aa1c7aa33f01bdbda59c328be432",
    "cross_cats_sorted": [
      "cs.CC",
      "math.AT"
    ],
    "license": "",
    "primary_cat": "cs.CG",
    "submitted_at": "2007-09-16T20:48:49Z",
    "title_canon_sha256": "25aaf2b42466c6455aa59b7be7ac95967d3b5ce4786620c10588afd87c0d14c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.2512",
    "kind": "arxiv",
    "version": 2
  }
}