Pith Number

pith:QL6COBQC

pith:2016:QL6COBQCNES7Y62OORP5OUJWOR

not attested not anchored not stored refs pending

Explicit Serre weights for two-dimensional Galois representations

Frank Calegari, Lambros Mavrides, Matthew Emerton, Toby Gee

arxiv:1608.06059 v2 · 2016-08-22 · 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{QL6COBQCNES7Y62OORP5OUJWOR}

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	2026-05-17T23:53:13.046914Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82fc2706026925fc7b4e745fd7513674668a97f23b1967c22cc743822ccd2584

Aliases

arxiv: 1608.06059 · arxiv_version: 1608.06059v2 · doi: 10.48550/arxiv.1608.06059 · pith_short_12: QL6COBQCNES7 · pith_short_16: QL6COBQCNES7Y62O · pith_short_8: QL6COBQC

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/QL6COBQCNES7Y62OORP5OUJWOR \
  | 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: 82fc2706026925fc7b4e745fd7513674668a97f23b1967c22cc743822ccd2584

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "872c7c132d21ecf93c524d3ac69d2092e1d77da305d5efcf44dbe668b42138c9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-08-22T06:18:59Z",
    "title_canon_sha256": "1dd4d59b646e9d5f276e0f247d53fd3abf8562881af85254696344d0a366f850"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.06059",
    "kind": "arxiv",
    "version": 2
  }
}