Pith Number

pith:IHUB5ZLD

pith:2004:IHUB5ZLDBWMWFCJF6DB2GTHZND

not attested not anchored not stored refs pending

Universal Characteristic Factors and Furstenberg Averages

Tamar Ziegler

arxiv:math/0403212 v2 · 2004-03-12 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IHUB5ZLDBWMWFCJF6DB2GTHZND}

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	2026-05-18T04:05:16.790372Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

41e81ee5630d99628925f0c3a34cf968d1fefcea5a3175727bc91f8c8b049ccf

Aliases

arxiv: math/0403212 · arxiv_version: math/0403212v2 · doi: 10.48550/arxiv.math/0403212 · pith_short_12: IHUB5ZLDBWMW · pith_short_16: IHUB5ZLDBWMWFCJF · pith_short_8: IHUB5ZLD

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/IHUB5ZLDBWMWFCJF6DB2GTHZND \
  | 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: 41e81ee5630d99628925f0c3a34cf968d1fefcea5a3175727bc91f8c8b049ccf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f2622c733c5a9e400ce6223088252e99984595430edd9040cbcf66dd857bab8d",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2004-03-12T18:02:42Z",
    "title_canon_sha256": "922e83bee4324bd14b3ef2e141b2feab7c6b14e2d01dc4def7ef3881b22ff0c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0403212",
    "kind": "arxiv",
    "version": 2
  }
}