Pith Number

pith:TGK4ECWG

pith:1999:TGK4ECWG4DDHV37E45MLVYYCLP

not attested not anchored not stored refs pending

Modularity of fibres in rigid local systems

Henri Darmon

arxiv:math/9905208 v1 · 1999-05-01 · 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{TGK4ECWG4DDHV37E45MLVYYCLP}

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	2026-05-18T01:05:33.007434Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9995c20ac6e0c67aefe4e758bae3025be83ddbdf571d206f7e45d9ec5d8eb9d8

Aliases

arxiv: math/9905208 · arxiv_version: math/9905208v1 · doi: 10.48550/arxiv.math/9905208 · pith_short_12: TGK4ECWG4DDH · pith_short_16: TGK4ECWG4DDHV37E · pith_short_8: TGK4ECWG

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/TGK4ECWG4DDHV37E45MLVYYCLP \
  | 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: 9995c20ac6e0c67aefe4e758bae3025be83ddbdf571d206f7e45d9ec5d8eb9d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "15df9edb6746e466248ff66722eab610be62edae62bf25746853bfab179284c9",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "1999-05-01T00:00:00Z",
    "title_canon_sha256": "f46cf7b9d56cb8e5fc9f458d8930550d6a48d9a13e8fda30c2e2d24c13ac4a8a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9905208",
    "kind": "arxiv",
    "version": 1
  }
}