Pith Number

pith:AUC6WKCP

pith:2013:AUC6WKCPYZUFE2IETTRFCR5LXB

not attested not anchored not stored refs pending

Analytic expanding circle maps with explicit spectra

Julia Slipantschuk, Oscar F. Bandtlow, Wolfram Just

arxiv:1306.0445 v1 · 2013-06-03 · math.DS · math.SP · nlin.CD

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AUC6WKCPYZUFE2IETTRFCR5LXB}

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	2026-05-18T01:49:33.705687Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0505eb284fc6685269049ce25147abb858c8d5ca2f038351079424831966c477

Aliases

arxiv: 1306.0445 · arxiv_version: 1306.0445v1 · doi: 10.48550/arxiv.1306.0445 · pith_short_12: AUC6WKCPYZUF · pith_short_16: AUC6WKCPYZUFE2IE · pith_short_8: AUC6WKCP

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/AUC6WKCPYZUFE2IETTRFCR5LXB \
  | 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: 0505eb284fc6685269049ce25147abb858c8d5ca2f038351079424831966c477

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a131c2665d975650fba640f38cad843dc9ca39e7f082981af86e86f855063b37",
    "cross_cats_sorted": [
      "math.SP",
      "nlin.CD"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-06-03T14:57:34Z",
    "title_canon_sha256": "8575a6c95429145e45d62b361092a5bab25b5f7e94e17c20a0d01d69764bf12c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.0445",
    "kind": "arxiv",
    "version": 1
  }
}