Pith Number

pith:L4KJHF2I

pith:2015:L4KJHF2IMDOQ3EGZQV2L5QVTIJ

not attested not anchored not stored refs pending

On topological lower bounds for algebraic computation trees

Andrei Gabrielov, Nicolai Vorobjov

arxiv:1502.04341 v2 · 2015-02-15 · cs.CC · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L4KJHF2IMDOQ3EGZQV2L5QVTIJ}

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	2026-05-18T01:35:16.173157Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f1493974860dd0d90d98574bec2b34270029694e7db1d8ce1dd9313c2937e80

Aliases

arxiv: 1502.04341 · arxiv_version: 1502.04341v2 · doi: 10.48550/arxiv.1502.04341 · pith_short_12: L4KJHF2IMDOQ · pith_short_16: L4KJHF2IMDOQ3EGZ · pith_short_8: L4KJHF2I

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/L4KJHF2IMDOQ3EGZQV2L5QVTIJ \
  | 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: 5f1493974860dd0d90d98574bec2b34270029694e7db1d8ce1dd9313c2937e80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc9409e5c74b52072aecb1d5a7d58f5291d05ed61a26db8ccf857224c6cb7e52",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2015-02-15T18:03:11Z",
    "title_canon_sha256": "5199f7bbdd655a5c23ed452ec1ee4748b54da08cfd9a29efc4e4be947d0857e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.04341",
    "kind": "arxiv",
    "version": 2
  }
}