Pith Number

pith:AF4XPURM

pith:2025:AF4XPURMSWPR2LGM57D7EO4QV7

not attested not anchored not stored refs pending

Inducing spectral gaps for the cohomological Laplacians of $\operatorname{Sp}_{2n}(\mathbb{Z})$

Jakub Szyma\'nski, Piotr Mizerka

arxiv:2504.16625 v1 · 2025-04-23 · math.GR · math.FA · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AF4XPURMSWPR2LGM57D7EO4QV7}

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	2026-07-05T10:53:02.302433Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

017977d22c959f1d2cccefc7f23b90aff42b059ee456b7c6ae376e880c794447

Aliases

arxiv: 2504.16625 · arxiv_version: 2504.16625v1 · doi: 10.48550/arxiv.2504.16625 · pith_short_12: AF4XPURMSWPR · pith_short_16: AF4XPURMSWPR2LGM · pith_short_8: AF4XPURM

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/AF4XPURMSWPR2LGM57D7EO4QV7 \
  | 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: 017977d22c959f1d2cccefc7f23b90aff42b059ee456b7c6ae376e880c794447

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5261808f10e5bc02a961d18842b55d4d333d289a96d7d35b9dd01657d3f65fb",
    "cross_cats_sorted": [
      "math.FA",
      "math.OA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2025-04-23T11:31:53Z",
    "title_canon_sha256": "aa7ba4bc87e9af804e7ea6e9763a4197ed29e2bc7781f3d090c1b94e97c6da07"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2504.16625",
    "kind": "arxiv",
    "version": 1
  }
}