Pith Number

pith:6ZK37UEK

pith:2026:6ZK37UEKY25PZOFCJ22XND2Z6D

not attested not anchored not stored refs pending

Exact Self-Imaging with Arbitrary Revival Spacings

Layton A. Hall, Samuel Alperin

arxiv:2601.08020 v3 · 2026-01-12 · physics.optics

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6ZK37UEKY25PZOFCJ22XND2Z6D}

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	2026-06-09T02:08:37.083985Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f655bfd08ac6bafcb8a24eb5768f59f0c3730c97b9d4f6323bb188cee09512cf

Aliases

arxiv: 2601.08020 · arxiv_version: 2601.08020v3 · doi: 10.48550/arxiv.2601.08020 · pith_short_12: 6ZK37UEKY25P · pith_short_16: 6ZK37UEKY25PZOFC · pith_short_8: 6ZK37UEK

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/6ZK37UEKY25PZOFCJ22XND2Z6D \
  | 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: f655bfd08ac6bafcb8a24eb5768f59f0c3730c97b9d4f6323bb188cee09512cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "133b3c06cb2bdfe80fb7ffef698be2b876acf766ee25cbef2b74a03b242f36d4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2026-01-12T21:52:08Z",
    "title_canon_sha256": "71e37fa9364f187817f3b76dfb8d946369dfc3858cd0ecb0353bc0bd91858eb1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.08020",
    "kind": "arxiv",
    "version": 3
  }
}