Pith Number

pith:P6RM2TBQ

pith:2009:P6RM2TBQBCQKV6LTUB44UOTFN2

not attested not anchored not stored refs pending

On surface subgroups of doubles of free groups

Cameron Gordon, Henry Wilton

arxiv:0902.3693 v1 · 2009-02-21 · 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{P6RM2TBQBCQKV6LTUB44UOTFN2}

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	2026-05-18T02:58:10.641068Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7fa2cd4c3008a0aaf973a079ca3a656eb49d69724b71d23be274f9f0801a5e50

Aliases

arxiv: 0902.3693 · arxiv_version: 0902.3693v1 · doi: 10.48550/arxiv.0902.3693 · pith_short_12: P6RM2TBQBCQK · pith_short_16: P6RM2TBQBCQKV6LT · pith_short_8: P6RM2TBQ

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/P6RM2TBQBCQKV6LTUB44UOTFN2 \
  | 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: 7fa2cd4c3008a0aaf973a079ca3a656eb49d69724b71d23be274f9f0801a5e50

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c37e998c06d16527843dc94b85ea2e822777c0a501b041d611516fdf985cf516",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-02-21T20:35:13Z",
    "title_canon_sha256": "fdecf033a5300063b5da61bdaf6332922980dc96370616267bd8e168fcbbc9c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.3693",
    "kind": "arxiv",
    "version": 1
  }
}