Pith Number

pith:UN6Q73GH

pith:2007:UN6Q73GHMLPIL6OND6TM323MW2

not attested not anchored not stored refs pending

Freiheitss\"{a}tze for one-relator quotients of surface groups and of limit groups

James Howie, Muhammad Sarwar Saeed

arxiv:0709.0416 v1 · 2007-09-04 · 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{UN6Q73GHMLPIL6OND6TM323MW2}

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	2026-05-18T04:33:36.789363Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a37d0fecc762de85f9cd1fa6cdeb6cb6abf2661ec5e02695eacd2ea787134cc8

Aliases

arxiv: 0709.0416 · arxiv_version: 0709.0416v1 · doi: 10.48550/arxiv.0709.0416 · pith_short_12: UN6Q73GHMLPI · pith_short_16: UN6Q73GHMLPIL6ON · pith_short_8: UN6Q73GH

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/UN6Q73GHMLPIL6OND6TM323MW2 \
  | 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: a37d0fecc762de85f9cd1fa6cdeb6cb6abf2661ec5e02695eacd2ea787134cc8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61a9f8094358934a0b68a941e2ada89de9651ac0a4f14c48b7cface703bd21bc",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2007-09-04T12:48:30Z",
    "title_canon_sha256": "00f4168dc9523f1c12b703fe1b3f90ea7c2eeda19bff94ee67228a514818a139"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.0416",
    "kind": "arxiv",
    "version": 1
  }
}