Pith Number

pith:4TE54PMX

pith:2006:4TE54PMXFNHO6Y4EYX3VEQYUPJ

not attested not anchored not stored refs pending

On Albanese torsors and the elementary obstruction

Olivier Wittenberg

arxiv:math/0611284 v2 · 2006-11-09 · math.AG · 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{4TE54PMXFNHO6Y4EYX3VEQYUPJ}

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	2026-05-18T01:18:10.561625Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4c9de3d972b4eef6384c5f75243147a43bb28a3c1478c6a40095c6e1b750e63

Aliases

arxiv: math/0611284 · arxiv_version: math/0611284v2 · doi: 10.48550/arxiv.math/0611284 · pith_short_12: 4TE54PMXFNHO · pith_short_16: 4TE54PMXFNHO6Y4E · pith_short_8: 4TE54PMX

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/4TE54PMXFNHO6Y4EYX3VEQYUPJ \
  | 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: e4c9de3d972b4eef6384c5f75243147a43bb28a3c1478c6a40095c6e1b750e63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c64ff11f7a0c9dc01317bcb2b514f85b224a1a35545e288c2acb62ca2bf63ae2",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2006-11-09T17:32:16Z",
    "title_canon_sha256": "aa84c259bb3bb3e84db08ce8d7f7cc1e18f696819dafe1ec8c62adcbf9830fe7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0611284",
    "kind": "arxiv",
    "version": 2
  }
}