Pith Number

pith:EPGTFVMM

pith:2011:EPGTFVMMY4CV4UJL5A5WOOT5MA

not attested not anchored not stored refs pending

Spheres in the curve complex

Howard Masur, Moon Duchin, Spencer Dowdall

arxiv:1109.6338 v2 · 2011-09-28 · math.GT · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EPGTFVMMY4CV4UJL5A5WOOT5MA}

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	2026-05-18T03:56:45.059620Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

23cd32d58cc7055e512be83b673a7d60064b5b5dd76bb5e900e873c5cdc90a56

Aliases

arxiv: 1109.6338 · arxiv_version: 1109.6338v2 · doi: 10.48550/arxiv.1109.6338 · pith_short_12: EPGTFVMMY4CV · pith_short_16: EPGTFVMMY4CV4UJL · pith_short_8: EPGTFVMM

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/EPGTFVMMY4CV4UJL5A5WOOT5MA \
  | 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: 23cd32d58cc7055e512be83b673a7d60064b5b5dd76bb5e900e873c5cdc90a56

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "435c52ca4719a61e34c8b4063e59a72e6d7bf0362018b9d58e5229f4244337d8",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-09-28T20:09:36Z",
    "title_canon_sha256": "8496d248dd22d4e3452eb24827b629fa1c77af7ab02b976767aee2416dfe1ad0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.6338",
    "kind": "arxiv",
    "version": 2
  }
}