Pith Number

pith:PMMFC3DD

pith:2015:PMMFC3DDEKMT3Q6UPNQNUMMWWD

not attested not anchored not stored refs pending

The partial captivity condition for U(1) extensions of expanding maps on the circle

Jens Wittsten, Masato Tsujii, Yushi Nakano

arxiv:1511.03817 v2 · 2015-11-12 · 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{PMMFC3DDEKMT3Q6UPNQNUMMWWD}

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	2026-05-18T01:12:43.356243Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b18516c6322993dc3d47b60da3196b0fcfdd1ed6f1d893bfbc5ba4f80fb18b3

Aliases

arxiv: 1511.03817 · arxiv_version: 1511.03817v2 · doi: 10.48550/arxiv.1511.03817 · pith_short_12: PMMFC3DDEKMT · pith_short_16: PMMFC3DDEKMT3Q6U · pith_short_8: PMMFC3DD

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/PMMFC3DDEKMT3Q6UPNQNUMMWWD \
  | 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: 7b18516c6322993dc3d47b60da3196b0fcfdd1ed6f1d893bfbc5ba4f80fb18b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9da95a620e1ff79eca6d756f00175557b25d134f2d94f86d4e560cdcdd2a3082",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-11-12T08:51:16Z",
    "title_canon_sha256": "149fb9c2a14ebf7fbf0ae48a4bc571a0ee8d548dcb3676746dada1ec0fd4f34c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.03817",
    "kind": "arxiv",
    "version": 2
  }
}