Pith Number

pith:3LULCQY7

pith:2005:3LULCQY7K4J6CXNUYIQNQNOXSC

not attested not anchored not stored refs pending

Manifolds homotopy equivalent to P^n # P^n

James F. Davis, Jeremy Brookman, Qayum Khan

arxiv:math/0509053 v3 · 2005-09-02 · 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{3LULCQY7K4J6CXNUYIQNQNOXSC}

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	2026-05-18T01:14:36.647445Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dae8b1431f5713e15db4c220d835d7909e8890c363e824ce83994bfdbcbd34b3

Aliases

arxiv: math/0509053 · arxiv_version: math/0509053v3 · doi: 10.48550/arxiv.math/0509053 · pith_short_12: 3LULCQY7K4J6 · pith_short_16: 3LULCQY7K4J6CXNU · pith_short_8: 3LULCQY7

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/3LULCQY7K4J6CXNUYIQNQNOXSC \
  | 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: dae8b1431f5713e15db4c220d835d7909e8890c363e824ce83994bfdbcbd34b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "693673e046cc1a1e7144d895f47ac2b5a5f7b75e20670567a35d58bc031fa56f",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2005-09-02T18:48:39Z",
    "title_canon_sha256": "31e75585aebaa0566011235fac1ca2188f2f6c057a11a8c66d3b91e2771b567b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0509053",
    "kind": "arxiv",
    "version": 3
  }
}