Pith Number

pith:GKA4PBV7

pith:2012:GKA4PBV7BC66WK6JP32N4KSPKX

not attested not anchored not stored refs pending

Iwasawa theory for symmetric powers of CM modular forms at non-ordinary primes

Antonio Lei, Robert Harron

arxiv:1208.1278 v1 · 2012-08-06 · 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{GKA4PBV7BC66WK6JP32N4KSPKX}

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	2026-05-18T01:29:32.220619Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3281c786bf08bdeb2bc97ef4de2a4f55c0c0e27c02b88bca773676fda7fb1e55

Aliases

arxiv: 1208.1278 · arxiv_version: 1208.1278v1 · doi: 10.48550/arxiv.1208.1278 · pith_short_12: GKA4PBV7BC66 · pith_short_16: GKA4PBV7BC66WK6J · pith_short_8: GKA4PBV7

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/GKA4PBV7BC66WK6JP32N4KSPKX \
  | 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: 3281c786bf08bdeb2bc97ef4de2a4f55c0c0e27c02b88bca773676fda7fb1e55

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "902d42211599563125d355da4ee1604baf03b9681d99f883b0733c27375299b3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-08-06T20:55:10Z",
    "title_canon_sha256": "7aea4ccdc7b4c269f27862d0af21071e30283a549fd59283529f15903c10aac1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.1278",
    "kind": "arxiv",
    "version": 1
  }
}