Pith Number

pith:Q4HX5X5X

pith:2024:Q4HX5X5XYGOKCXD5LC4YNWCN7G

not attested not anchored not stored refs pending

Equivalence of sub-Laplacian on Polarized groups

Antoni Kijowski, Ben Warhurst, Sebastiano Nicolussi Golo

arxiv:2501.00576 v1 · 2024-12-31 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q4HX5X5XYGOKCXD5LC4YNWCN7G}

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	2026-07-05T09:56:07.734036Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

870f7edfb7c19ca15c7d58b986d84df98dd96f8079f90e38d2f93d412a954e82

Aliases

arxiv: 2501.00576 · arxiv_version: 2501.00576v1 · doi: 10.48550/arxiv.2501.00576 · pith_short_12: Q4HX5X5XYGOK · pith_short_16: Q4HX5X5XYGOKCXD5 · pith_short_8: Q4HX5X5X

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/Q4HX5X5XYGOKCXD5LC4YNWCN7G \
  | 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: 870f7edfb7c19ca15c7d58b986d84df98dd96f8079f90e38d2f93d412a954e82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ac8add77c58a7ea85ebcb715063a7a6079cbf6cd8aec4b603d2304610d6fff6",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2024-12-31T18:04:24Z",
    "title_canon_sha256": "4c40704d24e71a213ef5ff5604926a6287402ada2152bafeeefd60bc26bbb8b2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.00576",
    "kind": "arxiv",
    "version": 1
  }
}