Pith Number

pith:CP4LIUXS

pith:2013:CP4LIUXSJK5INAOIKUMUMT4N7S

not attested not anchored not stored refs pending

On cycles and coverings associated to a knot

Lilya Lyubich, Mikhail Lyubich

arxiv:1301.2205 v1 · 2013-01-10 · math.GT · 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{CP4LIUXSJK5INAOIKUMUMT4N7S}

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	2026-05-18T03:36:47.149428Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13f8b452f24aba8681c85519464f8dfc80191003e90ee8bafade81fcd6985b2d

Aliases

arxiv: 1301.2205 · arxiv_version: 1301.2205v1 · doi: 10.48550/arxiv.1301.2205 · pith_short_12: CP4LIUXSJK5I · pith_short_16: CP4LIUXSJK5INAOI · pith_short_8: CP4LIUXS

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/CP4LIUXSJK5INAOIKUMUMT4N7S \
  | 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: 13f8b452f24aba8681c85519464f8dfc80191003e90ee8bafade81fcd6985b2d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f410ed52ad259c956e0fbe61dc6f1afca34efe1115ba76634f7a12087b73f0c3",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-01-10T18:10:29Z",
    "title_canon_sha256": "e1d31d2ba433c61c16f8cda3b3c3e4a6a2f1dc3ca43ead72161c435058aba8e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.2205",
    "kind": "arxiv",
    "version": 1
  }
}