Pith Number

pith:TUFC7NN3

pith:2012:TUFC7NN3VSAD4T72USGSIQZMA6

not attested not anchored not stored refs pending

Trivalent expanders and hyperbolic surfaces

Alina Vdovina, Ioannis Ivrissimtzis, Norbert Peyerimhoff

arxiv:1202.2304 v1 · 2012-02-10 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TUFC7NN3VSAD4T72USGSIQZMA6}

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	2026-05-18T04:02:36.749718Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d0a2fb5bbac803e4ffaa48d24432c079a8dea12780867742b3bd916c79b6a17

Aliases

arxiv: 1202.2304 · arxiv_version: 1202.2304v1 · doi: 10.48550/arxiv.1202.2304 · pith_short_12: TUFC7NN3VSAD · pith_short_16: TUFC7NN3VSAD4T72 · pith_short_8: TUFC7NN3

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/TUFC7NN3VSAD4T72USGSIQZMA6 \
  | 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: 9d0a2fb5bbac803e4ffaa48d24432c079a8dea12780867742b3bd916c79b6a17

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4735f9dc0296f35ff370d6d5884c04055ce5284d2af87d9c7eaf2cb72690b50",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-02-10T16:52:12Z",
    "title_canon_sha256": "b4b516db95b3f108dacbb457db58d7aca4cb5e87370b444f0e2af53ef9f39ee6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.2304",
    "kind": "arxiv",
    "version": 1
  }
}