Pith Number

pith:4NWI6BFL

pith:2015:4NWI6BFLOSABUE4XH5IE62P5UX

not attested not anchored not stored refs pending

Topological lower bounds for arithmetic networks

Andrei Gabrielov, Nicolai Vorobjov

arxiv:1510.03387 v3 · 2015-10-12 · cs.CC · 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{4NWI6BFLOSABUE4XH5IE62P5UX}

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	2026-05-18T01:11:08.447376Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e36c8f04ab74801a13973f504f69fda5c5153430f82363e7a0a53420e57c0c5b

Aliases

arxiv: 1510.03387 · arxiv_version: 1510.03387v3 · doi: 10.48550/arxiv.1510.03387 · pith_short_12: 4NWI6BFLOSAB · pith_short_16: 4NWI6BFLOSABUE4X · pith_short_8: 4NWI6BFL

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/4NWI6BFLOSABUE4XH5IE62P5UX \
  | 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: e36c8f04ab74801a13973f504f69fda5c5153430f82363e7a0a53420e57c0c5b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bca44684fe147fb044ae824971f8ff60d9d63ac74d7a74532bb83b5feec3bd6e",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2015-10-12T18:45:54Z",
    "title_canon_sha256": "161f420e98cc7f152a59f81a839befeb612c5eb28b1ac65f4d59ebfc0908836d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.03387",
    "kind": "arxiv",
    "version": 3
  }
}