Pith Number

pith:UDXKGT2S

pith:2011:UDXKGT2SECLYSMOZOWKVFCRKUN

not attested not anchored not stored refs pending

Certifying incompressibility of non-injective surfaces with scl

Danny Calegari

arxiv:1112.1791 v2 · 2011-12-08 · 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{UDXKGT2SECLYSMOZOWKVFCRKUN}

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	2026-05-18T03:27:52.431804Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a0eea34f5220978931d97595528a2aa343f4dbd8a773cafd7c306dfe5fa7d945

Aliases

arxiv: 1112.1791 · arxiv_version: 1112.1791v2 · doi: 10.48550/arxiv.1112.1791 · pith_short_12: UDXKGT2SECLY · pith_short_16: UDXKGT2SECLYSMOZ · pith_short_8: UDXKGT2S

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/UDXKGT2SECLYSMOZOWKVFCRKUN \
  | 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: a0eea34f5220978931d97595528a2aa343f4dbd8a773cafd7c306dfe5fa7d945

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3163ff33de22fb2ae7d765d1ca1d72ec261ace49945cae452604317680412527",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-12-08T09:25:43Z",
    "title_canon_sha256": "e248f69b98e2c4ae205a20bd2b743689f69bc7f9d17fc6a94b0e024c33b93aad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.1791",
    "kind": "arxiv",
    "version": 2
  }
}