Pith Number

pith:OK36IT5T

pith:2002:OK36IT5TQFYV4ONAC7MS3QJ3DI

not attested not anchored not stored refs pending

Hilbert series of fiber cones of ideals of almost minimal mixed multiplicity

Clare D'Cruz, J. K. Verma

arxiv:math/0212135 v1 · 2002-12-10 · math.AC · 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{OK36IT5TQFYV4ONAC7MS3QJ3DI}

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	2026-05-18T01:05:29.204753Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

72b7e44fb381715e39a017d92dc13b1a2a177421c5a9a567d33f8ace0e15eac3

Aliases

arxiv: math/0212135 · arxiv_version: math/0212135v1 · doi: 10.48550/arxiv.math/0212135 · pith_short_12: OK36IT5TQFYV · pith_short_16: OK36IT5TQFYV4ONA · pith_short_8: OK36IT5T

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/OK36IT5TQFYV4ONAC7MS3QJ3DI \
  | 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: 72b7e44fb381715e39a017d92dc13b1a2a177421c5a9a567d33f8ace0e15eac3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a45db4003b7bd52a655d4f5afe1c2a5f408d4b56f884f2f349e7afa613496178",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.AC",
    "submitted_at": "2002-12-10T05:25:21Z",
    "title_canon_sha256": "304bc7bcb108c7bb8b955ad7b68524ba99a2cc3f26976536b5829c3268cbc79c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0212135",
    "kind": "arxiv",
    "version": 1
  }
}