Pith Number

pith:4M2F2QPN

pith:2011:4M2F2QPNA26C4OSAWP7BJGOYWY

not attested not anchored not stored refs pending

Translation invariant equations and the method of Sanders

Thomas Bloom

arxiv:1107.1110 v2 · 2011-07-06 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4M2F2QPNA26C4OSAWP7BJGOYWY}

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	2026-05-18T03:40:14.491604Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3345d41ed06bc2e3a40b3fe1499d8b616274a2db2eb2ce16ae1c1f51453ec35

Aliases

arxiv: 1107.1110 · arxiv_version: 1107.1110v2 · doi: 10.48550/arxiv.1107.1110 · pith_short_12: 4M2F2QPNA26C · pith_short_16: 4M2F2QPNA26C4OSA · pith_short_8: 4M2F2QPN

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/4M2F2QPNA26C4OSAWP7BJGOYWY \
  | 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: e3345d41ed06bc2e3a40b3fe1499d8b616274a2db2eb2ce16ae1c1f51453ec35

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c339f8cd9081fe6ccd1525499794bf4521b63755982d06df94e02d07169b0fb3",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-07-06T12:43:20Z",
    "title_canon_sha256": "bac79e86a56498c42ebfc68ae736451eda42deb3d5ae830dbe58d75c3e264624"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.1110",
    "kind": "arxiv",
    "version": 2
  }
}