Pith Number

pith:3UMYRM4D

pith:2018:3UMYRM4DRUJSUGGXAUQ2LW65R2

not attested not anchored not stored refs pending

Outer billiards with the dynamics of a standard shift on a finite number of invariant curves

Andrey E. Mironov, Lior Shalom, Misha Bialy

arxiv:1811.04981 v1 · 2018-11-12 · 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{3UMYRM4DRUJSUGGXAUQ2LW65R2}

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	2026-05-18T00:01:01.529043Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd1988b3838d132a18d70521a5dbdd8e8f7fd831c7484995a641543da921d957

Aliases

arxiv: 1811.04981 · arxiv_version: 1811.04981v1 · doi: 10.48550/arxiv.1811.04981 · pith_short_12: 3UMYRM4DRUJS · pith_short_16: 3UMYRM4DRUJSUGGX · pith_short_8: 3UMYRM4D

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/3UMYRM4DRUJSUGGXAUQ2LW65R2 \
  | 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: dd1988b3838d132a18d70521a5dbdd8e8f7fd831c7484995a641543da921d957

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41f97a2079ecb4a4d8518bd32f7e84d1e856aace9f06389c510782a690ad5dda",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2018-11-12T19:51:39Z",
    "title_canon_sha256": "6060ef81359fe998955f22edffdd10facd55e4c40783cbaa97381147cc8b8622"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.04981",
    "kind": "arxiv",
    "version": 1
  }
}