Pith Number

pith:ZKRE3NTP

pith:2015:ZKRE3NTP6RRZUXRX32UEOJO6AF

not attested not anchored not stored refs pending

Nontrivial paths and periodic orbits of the $T$-fractal billiard table

Michel L. Lapidus, Robert G. Niemeyer, Robyn L. Miller

arxiv:1503.08492 v3 · 2015-03-29 · 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{ZKRE3NTP6RRZUXRX32UEOJO6AF}

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	2026-05-18T01:10:54.405743Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

caa24db66ff4639a5e37dea84725de014692232f16d81389fe98fef5364294d4

Aliases

arxiv: 1503.08492 · arxiv_version: 1503.08492v3 · doi: 10.48550/arxiv.1503.08492 · pith_short_12: ZKRE3NTP6RRZ · pith_short_16: ZKRE3NTP6RRZUXRX · pith_short_8: ZKRE3NTP

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/ZKRE3NTP6RRZUXRX32UEOJO6AF \
  | 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: caa24db66ff4639a5e37dea84725de014692232f16d81389fe98fef5364294d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42a541316ab938fa8f130dbc35d4e8fb4894f33014eb915ef9cfe2b93a57030d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-03-29T20:44:24Z",
    "title_canon_sha256": "994f3d75752cd7517457cf610596ff8deac5d15172357bae69b36ff26cea4c76"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.08492",
    "kind": "arxiv",
    "version": 3
  }
}