Pith Number

pith:PI5CLILQ

pith:2024:PI5CLILQAZPKDFVSLWEWC7CXCC

not attested not anchored not stored refs pending

Adjoint $L$-functions, congruence ideals, and Selmer groups over $\mathrm{GL}_n$

Ho Leung Fong

arxiv:2409.14933 v4 · 2024-09-23 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PI5CLILQAZPKDFVSLWEWC7CXCC}

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	2026-06-05T01:15:11.720806Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a3a25a170065ea196b25d89617c57109092ff058ca54c1d35814e02c0bba1e0

Aliases

arxiv: 2409.14933 · arxiv_version: 2409.14933v4 · doi: 10.48550/arxiv.2409.14933 · pith_short_12: PI5CLILQAZPK · pith_short_16: PI5CLILQAZPKDFVS · pith_short_8: PI5CLILQ

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/PI5CLILQAZPKDFVSLWEWC7CXCC \
  | 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: 7a3a25a170065ea196b25d89617c57109092ff058ca54c1d35814e02c0bba1e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4fd02c36969dd05f8d867d6721e000c1712457cd1196b5990ade07324c4f0c6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-09-23T11:41:10Z",
    "title_canon_sha256": "7b371342b56a9c3b876c8899bcb97b132376ec047d2608fac710a6075a740fe8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2409.14933",
    "kind": "arxiv",
    "version": 4
  }
}