Pith Number

pith:WVSN2GPE

pith:2011:WVSN2GPEUPR2TAPB2CWVBQCHY5

not attested not anchored not stored refs pending

IMPANGA lecture notes on log canonical thresholds

Mircea Mustata

arxiv:1107.2676 v1 · 2011-07-13 · math.AG · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WVSN2GPEUPR2TAPB2CWVBQCHY5}

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	2026-05-18T04:18:15.852829Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b564dd19e4a3e3a981e1d0ad50c047c74beb67aa2e162dd27e71293dfa0557e4

Aliases

arxiv: 1107.2676 · arxiv_version: 1107.2676v1 · doi: 10.48550/arxiv.1107.2676 · pith_short_12: WVSN2GPEUPR2 · pith_short_16: WVSN2GPEUPR2TAPB · pith_short_8: WVSN2GPE

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/WVSN2GPEUPR2TAPB2CWVBQCHY5 \
  | 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: b564dd19e4a3e3a981e1d0ad50c047c74beb67aa2e162dd27e71293dfa0557e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71c42099f24d42c007243b63459c24456dcbecaffd16e2e7af0189fafc27af0b",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-07-13T20:49:48Z",
    "title_canon_sha256": "6622a9c2bc07d4f3c137fc520b947628e2b4d8cfaecea0e62e5a2d095ce7faee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.2676",
    "kind": "arxiv",
    "version": 1
  }
}