Pith Number

pith:XRRZI4CB

pith:2014:XRRZI4CBDNCAZZKHU3UL7SOIOB

not attested not anchored not stored refs pending

Combinatorics of loop equations for branched covers of sphere

A. Popolitov, N. Orantin, P. Dunin-Barkowski, S. Shadrin

arxiv:1412.1698 v2 · 2014-12-04 · math-ph · math.CO · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XRRZI4CBDNCAZZKHU3UL7SOIOB}

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	2026-05-18T00:02:46.118220Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc639470411b440ce547a6e8bfc9c8704f97d5e699479c4aab263a9bc9a5e9b0

Aliases

arxiv: 1412.1698 · arxiv_version: 1412.1698v2 · doi: 10.48550/arxiv.1412.1698 · pith_short_12: XRRZI4CBDNCA · pith_short_16: XRRZI4CBDNCAZZKH · pith_short_8: XRRZI4CB

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/XRRZI4CBDNCAZZKHU3UL7SOIOB \
  | 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: bc639470411b440ce547a6e8bfc9c8704f97d5e699479c4aab263a9bc9a5e9b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "518bc58c5b34788361506f62bafec55606f0a495c93d6e648de389aeab068a66",
    "cross_cats_sorted": [
      "math.CO",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2014-12-04T15:26:32Z",
    "title_canon_sha256": "088cda67ac5555a6d9e660a65148c67c638bb4ff956c64071fb98dca2b1111d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.1698",
    "kind": "arxiv",
    "version": 2
  }
}