Pith Number

pith:NLHVN7L5

pith:2009:NLHVN7L5L6AIXMXAVTVAWKRNMY

not attested not anchored not stored refs pending

Geometric Auslander criterion for flatness

Edward Bierstone, Janusz Adamus, Pierre D. Milman

arxiv:0901.2744 v5 · 2009-01-18 · 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{NLHVN7L5L6AIXMXAVTVAWKRNMY}

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	2026-05-18T00:34:10.927510Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6acf56fd7d5f808bb2e0acea0b2a2d66036ae06684ec0e26d43a532f298438f4

Aliases

arxiv: 0901.2744 · arxiv_version: 0901.2744v5 · doi: 10.48550/arxiv.0901.2744 · pith_short_12: NLHVN7L5L6AI · pith_short_16: NLHVN7L5L6AIXMXA · pith_short_8: NLHVN7L5

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/NLHVN7L5L6AIXMXAVTVAWKRNMY \
  | 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: 6acf56fd7d5f808bb2e0acea0b2a2d66036ae06684ec0e26d43a532f298438f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "261924be40a057f1b067b204a3b3bf5c831b7bb902025530c065a466817fac7b",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2009-01-18T22:56:42Z",
    "title_canon_sha256": "dbea7e1de2b213ee3a57fafe7eeb497ac76b7dda242b410e16a67c00d3f9fc7b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0901.2744",
    "kind": "arxiv",
    "version": 5
  }
}