Pith Number

pith:Z7WFBD3E

pith:2016:Z7WFBD3EK6Z6RITN4XOP63WKBS

not attested not anchored not stored refs pending

Affine surfaces and their Veech groups

Charles Fougeron, Eduard Duryev, Selim Ghazouani

arxiv:1609.02130 v2 · 2016-09-07 · math.GT · 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{Z7WFBD3EK6Z6RITN4XOP63WKBS}

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	2026-05-18T00:59:19.386242Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfec508f6457b3e8a26de5dcff6eca0ca61835d8fd7c0ee976077e1af62f6928

Aliases

arxiv: 1609.02130 · arxiv_version: 1609.02130v2 · doi: 10.48550/arxiv.1609.02130 · pith_short_12: Z7WFBD3EK6Z6 · pith_short_16: Z7WFBD3EK6Z6RITN · pith_short_8: Z7WFBD3E

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/Z7WFBD3EK6Z6RITN4XOP63WKBS \
  | 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: cfec508f6457b3e8a26de5dcff6eca0ca61835d8fd7c0ee976077e1af62f6928

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1805e2bef54f3d303608978d846164a1b93e174fa3a5ff429fafbc8056edc800",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-09-07T19:33:52Z",
    "title_canon_sha256": "00aa75d5ad711b0584be26a77e6d7be966fbdc7cbe63e13b5becddb9c2c03920"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.02130",
    "kind": "arxiv",
    "version": 2
  }
}