Pith Number

pith:VTC3ZWVF

pith:2009:VTC3ZWVF6LV6I2LSJ5BT5D5HES

not attested not anchored not stored refs pending

Layered Tropical Mathematics

Louis Rowen, Manfred Knebusch, Zur Izhakian

arxiv:0912.1398 v3 · 2009-12-08 · math.AC · math.AG · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VTC3ZWVF6LV6I2LSJ5BT5D5HES}

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	2026-05-18T04:15:36.249931Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

acc5bcdaa5f2ebe469724f433e8fa724b83222d5fc6c9ed1e6abf79ed0c9d321

Aliases

arxiv: 0912.1398 · arxiv_version: 0912.1398v3 · doi: 10.48550/arxiv.0912.1398 · pith_short_12: VTC3ZWVF6LV6 · pith_short_16: VTC3ZWVF6LV6I2LS · pith_short_8: VTC3ZWVF

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/VTC3ZWVF6LV6I2LSJ5BT5D5HES \
  | 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: acc5bcdaa5f2ebe469724f433e8fa724b83222d5fc6c9ed1e6abf79ed0c9d321

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b323bd632d6923658686d0d9b34fc7d6cb5ce8e1278fc2fda4c9fea1ee4d7d8a",
    "cross_cats_sorted": [
      "math.AG",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2009-12-08T05:38:56Z",
    "title_canon_sha256": "c9e99556411d476f12b3f4a4617d274bd3e28fe24300dcc3d4588a717104a59b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.1398",
    "kind": "arxiv",
    "version": 3
  }
}