Pith Number

pith:JZRILSLM

pith:2021:JZRILSLM37FDWZUNI5SPYHGMMH

not attested not anchored not stored refs pending

On rationally integrable planar dual and projective billiards

Alexey Glutsyuk

arxiv:2112.07056 v4 · 2021-12-13 · math.DS · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JZRILSLM37FDWZUNI5SPYHGMMH}

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	2026-07-05T05:23:56.601889Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e6285c96cdfca3b668d4764fc1ccc61d36be0e5d1639e4c0740de436079d274

Aliases

arxiv: 2112.07056 · arxiv_version: 2112.07056v4 · doi: 10.48550/arxiv.2112.07056 · pith_short_12: JZRILSLM37FD · pith_short_16: JZRILSLM37FDWZUN · pith_short_8: JZRILSLM

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/JZRILSLM37FDWZUNI5SPYHGMMH \
  | 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: 4e6285c96cdfca3b668d4764fc1ccc61d36be0e5d1639e4c0740de436079d274

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bcac36ae5aaa7113b920a5330b708163429cf5ffe06d069b02a532a77abd29d1",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2021-12-13T22:48:30Z",
    "title_canon_sha256": "077f3fcb7e069921917ff51f7b36dbf2d8ead207a1a1168ebbd9d89e98f03fef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.07056",
    "kind": "arxiv",
    "version": 4
  }
}