Pith Number

pith:XU5CCUIP

pith:2025:XU5CCUIPDFKFIQ25MNLBAW2TBO

not attested not anchored not stored refs pending

Permutation-Based Distances for Groups and Group-Valued Time Series

Jos\'e M. Amig\'o, Roberto Dale

arxiv:2509.09191 v1 · 2025-09-11 · math-ph · 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{XU5CCUIPDFKFIQ25MNLBAW2TBO}

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	2026-07-05T12:09:31.283884Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd3a21510f195454435d6356105b530bb00ceee005ad25830d3dbd39749a2ab6

Aliases

arxiv: 2509.09191 · arxiv_version: 2509.09191v1 · doi: 10.48550/arxiv.2509.09191 · pith_short_12: XU5CCUIPDFKF · pith_short_16: XU5CCUIPDFKFIQ25 · pith_short_8: XU5CCUIP

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/XU5CCUIPDFKFIQ25MNLBAW2TBO \
  | 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: bd3a21510f195454435d6356105b530bb00ceee005ad25830d3dbd39749a2ab6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6403c7bf54038431496689592541d773d4015a45c5b9557feb331da598b64df4",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2025-09-11T07:02:48Z",
    "title_canon_sha256": "d7ec2ac239b458b25f2fb42b454726286f19effc502b94ab0b431c16931e2513"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.09191",
    "kind": "arxiv",
    "version": 1
  }
}