Pith Number

pith:6IQ6K2J3

pith:2007:6IQ6K2J3YXKRZCWOK4YWNHYUNF

not attested not anchored not stored refs pending

Examples of Free Actions on Products of Spheres

Ian Hambleton, Ozgun Unlu

arxiv:0705.4081 v2 · 2007-05-28 · 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{6IQ6K2J3YXKRZCWOK4YWNHYUNF}

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	2026-05-18T03:34:12.648277Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f221e5693bc5d51c8ace5731669f14694e9fdcce06082907c1cc348cf143b905

Aliases

arxiv: 0705.4081 · arxiv_version: 0705.4081v2 · doi: 10.48550/arxiv.0705.4081 · pith_short_12: 6IQ6K2J3YXKR · pith_short_16: 6IQ6K2J3YXKRZCWO · pith_short_8: 6IQ6K2J3

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/6IQ6K2J3YXKRZCWOK4YWNHYUNF \
  | 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: f221e5693bc5d51c8ace5731669f14694e9fdcce06082907c1cc348cf143b905

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e1f3f467b166af79daa29ab2e7b6dabf446ddd9609cfdd86b8eaed36fa52c51",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2007-05-28T17:51:54Z",
    "title_canon_sha256": "88cf463e49b312c8752dc3b4da7efc09c43b138754f0b044d45f20a978bc3aef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0705.4081",
    "kind": "arxiv",
    "version": 2
  }
}