Pith Number

pith:YILQNAQ3

pith:2009:YILQNAQ3EP6QAILWO64C6Y3NGP

not attested not anchored not stored refs pending

Stretching three-holed spheres and the Margulis invariant

Todd A. Drumm, Virginie Charette, William M. Goldman

arxiv:0907.0680 v1 · 2009-07-03 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YILQNAQ3EP6QAILWO64C6Y3NGP}

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	2026-05-18T04:18:34.928763Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c21706821b23fd00217677b82f636d33f31a48577756daa7406b85c15d142a06

Aliases

arxiv: 0907.0680 · arxiv_version: 0907.0680v1 · doi: 10.48550/arxiv.0907.0680 · pith_short_12: YILQNAQ3EP6Q · pith_short_16: YILQNAQ3EP6QAILW · pith_short_8: YILQNAQ3

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/YILQNAQ3EP6QAILWO64C6Y3NGP \
  | 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: c21706821b23fd00217677b82f636d33f31a48577756daa7406b85c15d142a06

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c0db10699cf2a1456e45fb850246264485470c2ae71007f87f14dc213c963af",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-07-03T18:17:36Z",
    "title_canon_sha256": "4b99cb0d3098455cdb669a5414ddbaa4c8ae17577f1485e299810099186db585"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.0680",
    "kind": "arxiv",
    "version": 1
  }
}