Pith Number

pith:ZTWWF35G

pith:2016:ZTWWF35GL4FRRBG53K65NCS22P

not attested not anchored not stored refs pending

Square-tiled surfaces of fixed combinatorial type: equidistribution, counting, volumes of the ambient strata

Anton Zorich, Elise Goujard, Peter Zograf, Vincent Delecroix

arxiv:1612.08374 v2 · 2016-12-26 · math.GT · math.CO · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZTWWF35GL4FRRBG53K65NCS22P}

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.

Cited by

1 paper in Pith

Complexity of Billiards in Polygons Associated to Hyperbolic $(p,q)$-Tilings

Receipt and verification

First computed	2026-05-17T23:50:07.602210Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cced62efa65f0b1884dddabdd68a5ad3d5725a4f108c79bbd08bee5927881a52

Aliases

arxiv: 1612.08374 · arxiv_version: 1612.08374v2 · doi: 10.48550/arxiv.1612.08374 · pith_short_12: ZTWWF35GL4FR · pith_short_16: ZTWWF35GL4FRRBG5 · pith_short_8: ZTWWF35G

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/ZTWWF35GL4FRRBG53K65NCS22P \
  | 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: cced62efa65f0b1884dddabdd68a5ad3d5725a4f108c79bbd08bee5927881a52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a6e1fa227a7468da1cbe4cf656ef88718b45b17b82f360be7b86ff329cff274",
    "cross_cats_sorted": [
      "math.CO",
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-12-26T13:08:12Z",
    "title_canon_sha256": "8b03909389b8f10a8f87afa219d748e9001e0f8d2bcf1d45682ae9d8dac8fd60"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.08374",
    "kind": "arxiv",
    "version": 2
  }
}