Pith Number

pith:7W6ORZUW

pith:2013:7W6ORZUWV3T7WZHVWAALRVTPFR

not attested not anchored not stored refs pending

On the modularity of reducible mod l Galois representations

Nicolas Billerey, Ricardo Menares

arxiv:1309.3717 v3 · 2013-09-15 · math.NT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7W6ORZUWV3T7WZHVWAALRVTPFR}

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	2026-05-18T00:46:32.327071Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fdbce8e696aee7fb64f5b000b8d66f2c5a0d8fbdacb82eb7b8cc4b13b14eefe7

Aliases

arxiv: 1309.3717 · arxiv_version: 1309.3717v3 · doi: 10.48550/arxiv.1309.3717 · pith_short_12: 7W6ORZUWV3T7 · pith_short_16: 7W6ORZUWV3T7WZHV · pith_short_8: 7W6ORZUW

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/7W6ORZUWV3T7WZHVWAALRVTPFR \
  | 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: fdbce8e696aee7fb64f5b000b8d66f2c5a0d8fbdacb82eb7b8cc4b13b14eefe7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1471738f971d3e5c1e7125b40b80302b3d840d0dddae99079d599df90cad1434",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-09-15T01:38:14Z",
    "title_canon_sha256": "0196048af162662eef7520e6a7d974b9aceca6713250ff3850160b43c3c2e36b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.3717",
    "kind": "arxiv",
    "version": 3
  }
}