Pith Number

pith:CD56F425

pith:2012:CD56F425MADOSQTYA4JHGM5KIZ

not attested not anchored not stored refs pending

Cartier's first theorem for Witt vectors on Z_{>= 0}^n - 0

Kirsten Wickelgren

arxiv:1211.1004 v2 · 2012-11-05 · math.KT · math.AT · 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{CD56F425MADOSQTYA4JHGM5KIZ}

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	2026-05-18T03:05:01.617438Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10fbe2f35d6006e9427807127333aa4666cbe736af46852519951ad1d78f49c5

Aliases

arxiv: 1211.1004 · arxiv_version: 1211.1004v2 · doi: 10.48550/arxiv.1211.1004 · pith_short_12: CD56F425MADO · pith_short_16: CD56F425MADOSQTY · pith_short_8: CD56F425

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/CD56F425MADOSQTYA4JHGM5KIZ \
  | 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: 10fbe2f35d6006e9427807127333aa4666cbe736af46852519951ad1d78f49c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "212e78d9e196418f86f925eb2f1a23806053831a6a76eb448efe94f34ad6356d",
    "cross_cats_sorted": [
      "math.AT",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2012-11-05T20:57:29Z",
    "title_canon_sha256": "b0fe75504a9456509775d36531326bf6a2342284195d7ad65211a8138cb259e3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.1004",
    "kind": "arxiv",
    "version": 2
  }
}