Pith Number

pith:CUKQQOFK

pith:2011:CUKQQOFKKALBCBOGUSE4SYT5TT

not attested not anchored not stored refs pending

Affine open subsets in A^3 without the cancellation property

Adrien Dubouloz (IMB)

arxiv:1107.1968 v1 · 2011-07-11 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CUKQQOFKKALBCBOGUSE4SYT5TT}

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	2026-05-18T04:18:33.733716Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15150838aa50161105c6a489c9627d9cf9675035c303ec7084bfc5ac665a1603

Aliases

arxiv: 1107.1968 · arxiv_version: 1107.1968v1 · doi: 10.48550/arxiv.1107.1968 · pith_short_12: CUKQQOFKKALB · pith_short_16: CUKQQOFKKALBCBOG · pith_short_8: CUKQQOFK

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/CUKQQOFKKALBCBOGUSE4SYT5TT \
  | 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: 15150838aa50161105c6a489c9627d9cf9675035c303ec7084bfc5ac665a1603

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8fe259a83bcde6431c7e8d1973ef3102e1ae4f67adb7bb8c03feb3e41f242cac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-07-11T08:56:19Z",
    "title_canon_sha256": "63b47f9bcbcebcf83e1bc4368c78799fd94af71cc5063faf08271b3b93feeeb5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.1968",
    "kind": "arxiv",
    "version": 1
  }
}