Pith Number

pith:AXQXBHR4

pith:2008:AXQXBHR4Z43VPLYKNTAEI3DTFP

not attested not anchored not stored refs pending

The basic geometry of Witt vectors, I: The affine case

James Borger

arxiv:0801.1691 v6 · 2008-01-10 · math.AG · math.CT · 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{AXQXBHR4Z43VPLYKNTAEI3DTFP}

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	2026-05-18T01:24:31.205560Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05e1709e3ccf3757af0a6cc0446c732bc5cc7cb0060d9fc409cbc73ad0c790f9

Aliases

arxiv: 0801.1691 · arxiv_version: 0801.1691v6 · doi: 10.48550/arxiv.0801.1691 · pith_short_12: AXQXBHR4Z43V · pith_short_16: AXQXBHR4Z43VPLYK · pith_short_8: AXQXBHR4

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/AXQXBHR4Z43VPLYKNTAEI3DTFP \
  | 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: 05e1709e3ccf3757af0a6cc0446c732bc5cc7cb0060d9fc409cbc73ad0c790f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e63ad6999c3ad473e7953937ff3d9e513d68c2f77586f9ad3d023cf2f6f21bed",
    "cross_cats_sorted": [
      "math.CT",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2008-01-10T21:59:44Z",
    "title_canon_sha256": "0eb84486cc76045e903eff056fff5e210c6133ad7c159ed28f51b7089a4096a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0801.1691",
    "kind": "arxiv",
    "version": 6
  }
}