Pith Number

pith:SB6X5ESP

pith:2011:SB6X5ESPBJJABHU4VKMWZZAEKZ

not attested not anchored not stored refs pending

Surpassing the Ratios Conjecture in the 1-level density of Dirichlet $L$-functions

Daniel Fiorilli, Steven J. Miller

arxiv:1111.3896 v3 · 2011-11-16 · 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{SB6X5ESPBJJABHU4VKMWZZAEKZ}

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	2026-05-18T01:22:28.813787Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

907d7e924f0a52009e9caa996ce40456612fd9bc4176a1fa254276b7313c979e

Aliases

arxiv: 1111.3896 · arxiv_version: 1111.3896v3 · doi: 10.48550/arxiv.1111.3896 · pith_short_12: SB6X5ESPBJJA · pith_short_16: SB6X5ESPBJJABHU4 · pith_short_8: SB6X5ESP

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/SB6X5ESPBJJABHU4VKMWZZAEKZ \
  | 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: 907d7e924f0a52009e9caa996ce40456612fd9bc4176a1fa254276b7313c979e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a90502b50c5ccf1b106f0c02270f89e0ae13f07f7f2ec2f33a0c8c802a5c3b6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-11-16T18:14:14Z",
    "title_canon_sha256": "11a9730ce444a8761f6240eb298ba9b77a98dbd47f2dd65e5beeab5cf6c50197"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.3896",
    "kind": "arxiv",
    "version": 3
  }
}