Pith Number

pith:BB5FIGIE

pith:2008:BB5FIGIEHIBFED2TGK4FMPCZU3

not attested not anchored not stored refs pending

Cohomology rings of almost-direct products of free groups

Daniel C. Cohen

arxiv:0811.1330 v1 · 2008-11-09 · math.AT · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BB5FIGIEHIBFED2TGK4FMPCZU3}

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	2026-05-17T23:53:39.457570Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

087a5419043a02520f5332b8563c59a6dcc940b3025e1dfef13fae4d2d724904

Aliases

arxiv: 0811.1330 · arxiv_version: 0811.1330v1 · doi: 10.48550/arxiv.0811.1330 · pith_short_12: BB5FIGIEHIBF · pith_short_16: BB5FIGIEHIBFED2T · pith_short_8: BB5FIGIE

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/BB5FIGIEHIBFED2TGK4FMPCZU3 \
  | 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: 087a5419043a02520f5332b8563c59a6dcc940b3025e1dfef13fae4d2d724904

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c717c84ec9d4d13655e252485cf401dbc64cf172a8dc4e8bf2f4d7417b5dc7b",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2008-11-09T12:05:48Z",
    "title_canon_sha256": "2de91203e265a3999d99d803fbab497e1837875f0077d823c5263dd303fcca22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0811.1330",
    "kind": "arxiv",
    "version": 1
  }
}