Pith Number

pith:3BGPKA3A

pith:2026:3BGPKA3AXJZLLRXBPDU6Y4NQCF

not attested not anchored not stored refs pending

Symplectic billiards as Minkowski billiards

Ana Chavez Caliz, Peter Albers, Serge Tabachnikov

arxiv:2607.05986 v1 · 2026-07-07 · math.DS · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3BGPKA3AXJZLLRXBPDU6Y4NQCF}

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	2026-07-08T01:18:52.471565Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d84cf50360ba72b5c6e178e9ec71b0116711f8cdcf873ad157dc96197ab3050e

Aliases

arxiv: 2607.05986 · arxiv_version: 2607.05986v1 · doi: 10.48550/arxiv.2607.05986 · pith_short_12: 3BGPKA3AXJZL · pith_short_16: 3BGPKA3AXJZLLRXB · pith_short_8: 3BGPKA3A

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/3BGPKA3AXJZLLRXBPDU6Y4NQCF \
  | 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: d84cf50360ba72b5c6e178e9ec71b0116711f8cdcf873ad157dc96197ab3050e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "928897e7cf1f21903f4586c99fe4e8e43c42d891d1c5e4a9e648feeba9a4f12f",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-07-07T08:18:41Z",
    "title_canon_sha256": "224b432c51b95fae798899d7a0be73f4d47c891f86b073a5109b18f1b388e456"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.05986",
    "kind": "arxiv",
    "version": 1
  }
}