Pith Number

pith:P5Z3Y5QT

pith:2011:P5Z3Y5QTIWXJLBB7AVJGTAIXQW

not attested not anchored not stored refs pending

Anisotropy and the integral closure

Michiel Kosters

arxiv:1109.6733 v1 · 2011-09-30 · math.AC · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P5Z3Y5QTIWXJLBB7AVJGTAIXQW}

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	2026-05-18T01:33:57.318573Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f73bc761345ae95843f0552698117859a6951f2a0d49d196eabae240eab4f59

Aliases

arxiv: 1109.6733 · arxiv_version: 1109.6733v1 · doi: 10.48550/arxiv.1109.6733 · pith_short_12: P5Z3Y5QTIWXJ · pith_short_16: P5Z3Y5QTIWXJLBB7 · pith_short_8: P5Z3Y5QT

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/P5Z3Y5QTIWXJLBB7AVJGTAIXQW \
  | 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: 7f73bc761345ae95843f0552698117859a6951f2a0d49d196eabae240eab4f59

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8bf1ebfb02097c950ea4b9597ddbd692bf4557bcd45438b61dd4c5cb8c9668cb",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-09-30T07:31:41Z",
    "title_canon_sha256": "ea23139e3b64875001035d8347e7658e8be2c7ceab47a416b402223185c0ffe4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.6733",
    "kind": "arxiv",
    "version": 1
  }
}