Pith Number

pith:KPZBITHO

pith:2012:KPZBITHOLRROKR4KRFWUW4KVDT

not attested not anchored not stored refs pending

Any finite group acts freely and homologically trivially on a product of spheres

James F. Davis

arxiv:1209.0370 v2 · 2012-09-03 · math.GT · math.AT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KPZBITHOLRROKR4KRFWUW4KVDT}

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	2026-05-18T01:25:55.984212Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53f2144cee5c62e5478a896d4b71551cd2fed8dd9f1b2ffaff99bbb968549485

Aliases

arxiv: 1209.0370 · arxiv_version: 1209.0370v2 · doi: 10.48550/arxiv.1209.0370 · pith_short_12: KPZBITHOLRRO · pith_short_16: KPZBITHOLRROKR4K · pith_short_8: KPZBITHO

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/KPZBITHOLRROKR4KRFWUW4KVDT \
  | 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: 53f2144cee5c62e5478a896d4b71551cd2fed8dd9f1b2ffaff99bbb968549485

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99fea25fd8a736a04e22e04f6148d1d91d4d989df7a99bd9d609a2d327a227d9",
    "cross_cats_sorted": [
      "math.AT",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-09-03T14:54:16Z",
    "title_canon_sha256": "bfb3aad5fbfecfa61af165a89e4dd5996a8d539e907a4a4522aa1b3af74aaf9f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0370",
    "kind": "arxiv",
    "version": 2
  }
}