Pith Number

pith:NMKRUIBS

pith:2003:NMKRUIBS6EWSIGELNHV2JLHAEF

not attested not anchored not stored refs pending

Some Examples of Free actions on Products of Spheres

Ian Hambleton

arxiv:math/0309152 v4 · 2003-09-08 · 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{NMKRUIBS6EWSIGELNHV2JLHAEF}

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	2026-05-18T03:34:00.547522Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b151a2032f12d24188b69eba4ace0216308d09d92b9a1b1ec015c6129620637

Aliases

arxiv: math/0309152 · arxiv_version: math/0309152v4 · doi: 10.48550/arxiv.math/0309152 · pith_short_12: NMKRUIBS6EWS · pith_short_16: NMKRUIBS6EWSIGEL · pith_short_8: NMKRUIBS

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/NMKRUIBS6EWSIGELNHV2JLHAEF \
  | 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: 6b151a2032f12d24188b69eba4ace0216308d09d92b9a1b1ec015c6129620637

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8366a38c1caebafc47a0d06e909d028dd057a7ffa3fbe3f845fccf70794dc750",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2003-09-08T19:22:59Z",
    "title_canon_sha256": "92dd9c240a15f386e3ed56ad5fad5b71125abd73d5402b0859f7aaa662b0f6c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0309152",
    "kind": "arxiv",
    "version": 4
  }
}