Pith Number

pith:6WL4INAL

pith:2010:6WL4INALYFXVJC5WA2FP7EU35A

not attested not anchored not stored refs pending

Wach modules and critical slope p-adic L-functions

David Loeffler, Sarah Livia Zerbes

arxiv:1012.0175 v1 · 2010-12-01 · 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{6WL4INALYFXVJC5WA2FP7EU35A}

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	2026-05-18T03:20:59.048723Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f597c4340bc16f548bb6068aff929be83091d3a732e6476f16a03aab5506742f

Aliases

arxiv: 1012.0175 · arxiv_version: 1012.0175v1 · doi: 10.48550/arxiv.1012.0175 · pith_short_12: 6WL4INALYFXV · pith_short_16: 6WL4INALYFXVJC5W · pith_short_8: 6WL4INAL

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/6WL4INALYFXVJC5WA2FP7EU35A \
  | 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: f597c4340bc16f548bb6068aff929be83091d3a732e6476f16a03aab5506742f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f82e096e1271f38c01d01ed5d0454bab5d2290bf5277996a8e90bd67700980e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-12-01T12:24:14Z",
    "title_canon_sha256": "e87a5e09a3db0aab612288e505c3407b54beb53c47472e3417f0112eed6dfdf3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0175",
    "kind": "arxiv",
    "version": 1
  }
}