Pith Number

pith:QNTMTXFX

pith:2011:QNTMTXFX6OZD3PJIRLLD3MY6YB

not attested not anchored not stored refs pending

An ampleness criterion with the extendability of singular positive metrics

Shin-ichi Matsumura

arxiv:1107.3223 v2 · 2011-07-16 · math.CV · 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{QNTMTXFX6OZD3PJIRLLD3MY6YB}

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	2026-05-18T03:36:25.348659Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8366c9dcb7f3b23dbd288ad63db31ec04574d57fd768be24d6a3dbab5b6900e6

Aliases

arxiv: 1107.3223 · arxiv_version: 1107.3223v2 · doi: 10.48550/arxiv.1107.3223 · pith_short_12: QNTMTXFX6OZD · pith_short_16: QNTMTXFX6OZD3PJI · pith_short_8: QNTMTXFX

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/QNTMTXFX6OZD3PJIRLLD3MY6YB \
  | 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: 8366c9dcb7f3b23dbd288ad63db31ec04574d57fd768be24d6a3dbab5b6900e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d0730f6524be3a68436a201faff66d6751959d4878921054626e27f91adead9",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2011-07-16T12:10:07Z",
    "title_canon_sha256": "720daa7b3dc44e0ec4914448e3a1153d15244bd1e32164f97a9f65d967df7c68"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.3223",
    "kind": "arxiv",
    "version": 2
  }
}