Pith Number

pith:3R7LSYWV

pith:2017:3R7LSYWVCJEXUDPTLOG4GCGC75

not attested not anchored not stored refs pending

The topological complexity of the free product

Alexander Dranishnikov, Rustam Sadykov

arxiv:1710.04711 v2 · 2017-10-12 · math.AT · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3R7LSYWVCJEXUDPTLOG4GCGC75}

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.

Cited by

1 paper in Pith

Configuration sets for groups

Receipt and verification

First computed	2026-05-18T00:31:35.556105Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc7eb962d512497a0df35b8dc308c2ff621905290f57449caec79e6a1b29bdf1

Aliases

arxiv: 1710.04711 · arxiv_version: 1710.04711v2 · doi: 10.48550/arxiv.1710.04711 · pith_short_12: 3R7LSYWVCJEX · pith_short_16: 3R7LSYWVCJEXUDPT · pith_short_8: 3R7LSYWV

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/3R7LSYWVCJEXUDPTLOG4GCGC75 \
  | 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: dc7eb962d512497a0df35b8dc308c2ff621905290f57449caec79e6a1b29bdf1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0c6f2a5940e05e0b7f0b57bd51bf5a6717e9f2cc71f4518d4c28be8366c6b74",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2017-10-12T20:38:20Z",
    "title_canon_sha256": "7441482f13a51175b6974b9c6f48d0b53bad06cc1f83a2a734c2318f15bf551a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.04711",
    "kind": "arxiv",
    "version": 2
  }
}