Pith Number

pith:CC7OLWZF

pith:2013:CC7OLWZFU7QPGDEKCF4BWJTJSP

not attested not anchored not stored refs pending

The circle method and bounds for $L$-functions - III: $t$-aspect subconvexity for GL(3) $L$-functions

Ritabrata Munshi

arxiv:1301.1007 v3 · 2013-01-06 · 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{CC7OLWZFU7QPGDEKCF4BWJTJSP}

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	2026-05-18T02:54:28.120647Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10bee5db25a7e0f30c8a11781b266993d15c88b892bbafeb4f98536b913b860a

Aliases

arxiv: 1301.1007 · arxiv_version: 1301.1007v3 · doi: 10.48550/arxiv.1301.1007 · pith_short_12: CC7OLWZFU7QP · pith_short_16: CC7OLWZFU7QPGDEK · pith_short_8: CC7OLWZF

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/CC7OLWZFU7QPGDEKCF4BWJTJSP \
  | 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: 10bee5db25a7e0f30c8a11781b266993d15c88b892bbafeb4f98536b913b860a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8fce1c769cfac39e94ee87e749bf7bdfa399f080b65148c48b9bde49377632d8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-01-06T13:54:16Z",
    "title_canon_sha256": "ef08de8ab82bb00029f19cc88fc5293c986798f68f391d5d09a6b86907977985"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.1007",
    "kind": "arxiv",
    "version": 3
  }
}