Pith Number

pith:K4YBA4WU

pith:2007:K4YBA4WUU4SJZFRQQCPH5HEDUQ

not attested not anchored not stored refs pending

Sets of double and triple weights of trees

Elena Rubei

arxiv:0712.3026 v3 · 2007-12-18 · 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{K4YBA4WUU4SJZFRQQCPH5HEDUQ}

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	2026-05-18T04:23:35.352789Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

57301072d4a7249c9630809e7e9c83a420f3c284154e6b65cc00623f30c31825

Aliases

arxiv: 0712.3026 · arxiv_version: 0712.3026v3 · doi: 10.48550/arxiv.0712.3026 · pith_short_12: K4YBA4WUU4SJ · pith_short_16: K4YBA4WUU4SJZFRQ · pith_short_8: K4YBA4WU

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/K4YBA4WUU4SJZFRQQCPH5HEDUQ \
  | 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: 57301072d4a7249c9630809e7e9c83a420f3c284154e6b65cc00623f30c31825

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d4db92fc5e61abf4b7996cd663c7ccc9159f30739172e2a46ef42ec48bf2eda",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2007-12-18T19:18:36Z",
    "title_canon_sha256": "2b5e39b1c8f9b4bd69c39bfec8b89039caec8a778786522c802ca3456f962bfb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.3026",
    "kind": "arxiv",
    "version": 3
  }
}