Pith Number

pith:Q6BWRWT7

pith:2012:Q6BWRWT7UL354SH64C2SV3723T

not attested not anchored not stored refs pending

Uniform Hyperbolicity of the Graphs of Curves

Tarik Aougab

arxiv:1212.3160 v2 · 2012-12-13 · math.GT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q6BWRWT7UL354SH64C2SV3723T}

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	2026-05-18T03:38:22.871386Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

878368da7fa2f7de48fee0b52aeffadcc09693edd5b8e026c639dbe0aac98078

Aliases

arxiv: 1212.3160 · arxiv_version: 1212.3160v2 · doi: 10.48550/arxiv.1212.3160 · pith_short_12: Q6BWRWT7UL35 · pith_short_16: Q6BWRWT7UL354SH6 · pith_short_8: Q6BWRWT7

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/Q6BWRWT7UL354SH64C2SV3723T \
  | 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: 878368da7fa2f7de48fee0b52aeffadcc09693edd5b8e026c639dbe0aac98078

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da02c70dff1479a14fb4743071d411505cdbfd676b5311507a8889d8426ee4be",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-12-13T12:56:35Z",
    "title_canon_sha256": "47c13dda49bbdd810311e604e59e4241090a39b5533c5e3993ee44ad7d786669"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.3160",
    "kind": "arxiv",
    "version": 2
  }
}