Pith Number

pith:QYWK3AOF

pith:2026:QYWK3AOFRMP4Q5S2LAZGRZ4BZR

not attested not anchored not stored refs pending

Equations in Products of Free Groups and 3-Manifold Groups, I

Alina Vdovina, Olga Kharlampovich

arxiv:2606.00335 v1 · 2026-05-29 · math.GR · 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{QYWK3AOFRMP4Q5S2LAZGRZ4BZR}

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	2026-06-02T01:03:51.921013Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

862cad81c58b1fc8765a583268e781cc4b35cf27edc72e2ee8857856e227c9fd

Aliases

arxiv: 2606.00335 · arxiv_version: 2606.00335v1 · doi: 10.48550/arxiv.2606.00335 · pith_short_12: QYWK3AOFRMP4 · pith_short_16: QYWK3AOFRMP4Q5S2 · pith_short_8: QYWK3AOF

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/QYWK3AOFRMP4Q5S2LAZGRZ4BZR \
  | 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: 862cad81c58b1fc8765a583268e781cc4b35cf27edc72e2ee8857856e227c9fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "259b0bfe137658e4868c745404535015871e09e0e34d10971ed56b58ecca7fe9",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-05-29T20:20:03Z",
    "title_canon_sha256": "40c2d8af083a77ed7108395e1e037b7a8cc53ccb35373afcd4ba90436560f6f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.00335",
    "kind": "arxiv",
    "version": 1
  }
}