Pith Number

pith:DSBOO5FA

pith:2015:DSBOO5FAK4UTBZQNVBSRIXPYX2

not attested not anchored not stored refs pending

Asymptotic Hilbert Polynomial and a bound for Waldschmidt constants

Halszka Tutaj-Gasinska, Lucja Farnik, Marcin Dumnicki

arxiv:1511.07633 v1 · 2015-11-24 · 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{DSBOO5FAK4UTBZQNVBSRIXPYX2}

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	2026-05-18T00:41:23.322459Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c82e774a0572930e60da865145df8bea0734c68b2efeec25fbb7f358ea304c2

Aliases

arxiv: 1511.07633 · arxiv_version: 1511.07633v1 · doi: 10.48550/arxiv.1511.07633 · pith_short_12: DSBOO5FAK4UT · pith_short_16: DSBOO5FAK4UTBZQN · pith_short_8: DSBOO5FA

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/DSBOO5FAK4UTBZQNVBSRIXPYX2 \
  | 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: 1c82e774a0572930e60da865145df8bea0734c68b2efeec25fbb7f358ea304c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47812abadbc066d6a1bd6d08099de7b4d42599cb80c0db2b23b09def56387074",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2015-11-24T10:26:18Z",
    "title_canon_sha256": "d09220d6ae4f4158a30fadc1e916a0b54b13fbd886c884c65f29c2534a0592df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.07633",
    "kind": "arxiv",
    "version": 1
  }
}