Pith Number

pith:7WXDKBAB

pith:2011:7WXDKBABDKUHGKWJD4T5VBI65Z

not attested not anchored not stored refs pending

An inductive analytic criterion for flatness

Edward Bierstone, Janusz Adamus, Pierre D. Milman

arxiv:1101.1938 v1 · 2011-01-10 · math.AC · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7WXDKBABDKUHGKWJD4T5VBI65Z}

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	2026-05-18T04:31:51.383944Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fdae3504011aa8732ac91f27da851eee5be8f0567ff8bb7205b18bc0a8402260

Aliases

arxiv: 1101.1938 · arxiv_version: 1101.1938v1 · doi: 10.48550/arxiv.1101.1938 · pith_short_12: 7WXDKBABDKUH · pith_short_16: 7WXDKBABDKUHGKWJ · pith_short_8: 7WXDKBAB

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/7WXDKBABDKUHGKWJD4T5VBI65Z \
  | 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: fdae3504011aa8732ac91f27da851eee5be8f0567ff8bb7205b18bc0a8402260

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63317aac8518ad3e34b1e45453f8639883a9e2f875b2b5fd922b43f3fe64dd16",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-01-10T20:11:51Z",
    "title_canon_sha256": "95911151e33c4bf0e14ba201e52c2a1a8d7d185bc9418846ffa375cb08845925"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.1938",
    "kind": "arxiv",
    "version": 1
  }
}