Pith Number

pith:TBZMN3YB

pith:2012:TBZMN3YBPQCVFSTIEN3KIZWRXT

not attested not anchored not stored refs pending

On metric relative hyperbolicity

Alessandro Sisto

arxiv:1210.8081 v1 · 2012-10-30 · 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{TBZMN3YBPQCVFSTIEN3KIZWRXT}

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	2026-05-18T03:41:57.103815Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9872c6ef017c0552ca682376a466d1bcfc3f373350440e21a8658a9a13661345

Aliases

arxiv: 1210.8081 · arxiv_version: 1210.8081v1 · doi: 10.48550/arxiv.1210.8081 · pith_short_12: TBZMN3YBPQCV · pith_short_16: TBZMN3YBPQCVFSTI · pith_short_8: TBZMN3YB

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/TBZMN3YBPQCVFSTIEN3KIZWRXT \
  | 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: 9872c6ef017c0552ca682376a466d1bcfc3f373350440e21a8658a9a13661345

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4847e8ca8755eacd808a6ee9f477cfb5b25217fcaefc16a71bd5884fbc59f3e3",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-10-30T16:53:53Z",
    "title_canon_sha256": "98aebf23bd87868258dd7600854e4e39dbd8c62ac366b59af8bf5bda3f3511cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.8081",
    "kind": "arxiv",
    "version": 1
  }
}