Pith Number

pith:GSXLI6UZ

pith:2024:GSXLI6UZNL7SV4NNGDF3VHW73R

not attested not anchored not stored refs pending

On the pro-modularity in the residually reducible case for some totally real fields

Xinyao Zhang

arxiv:2411.18661 v4 · 2024-11-27 · 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{GSXLI6UZNL7SV4NNGDF3VHW73R}

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	2026-07-05T11:41:19.796725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34aeb47a996aff2af1ad30cbba9edfdc4a357c4ab1c8338b85ef87316b01e791

Aliases

arxiv: 2411.18661 · arxiv_version: 2411.18661v4 · doi: 10.48550/arxiv.2411.18661 · pith_short_12: GSXLI6UZNL7S · pith_short_16: GSXLI6UZNL7SV4NN · pith_short_8: GSXLI6UZ

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/GSXLI6UZNL7SV4NNGDF3VHW73R \
  | 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: 34aeb47a996aff2af1ad30cbba9edfdc4a357c4ab1c8338b85ef87316b01e791

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc2d3217fcf83b1416b3705b10ec597196f5ccfbfe276f476a99a983d8d75389",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-11-27T12:50:38Z",
    "title_canon_sha256": "9cd394166550966d920974bb99adbb5f87f544e854758572b3dcb3c5862856ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.18661",
    "kind": "arxiv",
    "version": 4
  }
}