Pith Number

pith:YUTZGT6S

pith:2012:YUTZGT6SHBMUDOQR3SNO6M3GED

not attested not anchored not stored refs pending

The circle method and bounds for $L$-functions - II: Subconvexity for twists of GL(3) $L$-functions

Ritabrata Munshi

arxiv:1211.5731 v2 · 2012-11-25 · 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{YUTZGT6SHBMUDOQR3SNO6M3GED}

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	2026-05-18T03:36:06.152376Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c527934fd2385941ba11dc9aef336620f9a983787fef6cccf5e89038d19769f3

Aliases

arxiv: 1211.5731 · arxiv_version: 1211.5731v2 · doi: 10.48550/arxiv.1211.5731 · pith_short_12: YUTZGT6SHBMU · pith_short_16: YUTZGT6SHBMUDOQR · pith_short_8: YUTZGT6S

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/YUTZGT6SHBMUDOQR3SNO6M3GED \
  | 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: c527934fd2385941ba11dc9aef336620f9a983787fef6cccf5e89038d19769f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2fc2d1d69b088663da6003e8acb523184c4e76fb0f7e13f2a696f97087910fcf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-11-25T06:19:17Z",
    "title_canon_sha256": "5c0d63a189b2fa507d626e453de5a6754fe18e895cca9eab2374ef0d1d4347c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.5731",
    "kind": "arxiv",
    "version": 2
  }
}