Pith Number

pith:3ONB4G4S

pith:2006:3ONB4G4SPR4RVKUTP5OZPGJ2OD

not attested not anchored not stored refs pending

On the zeros of Eisenstein series for $\Gamma_0^* (5)$ and $\Gamma_0^* (7)$

Junichi Shigezumi

arxiv:math/0607409 v3 · 2006-07-18 · 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{3ONB4G4SPR4RVKUTP5OZPGJ2OD}

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	2026-05-18T02:56:12.953915Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db9a1e1b927c791aaa937f5d97993a70e1b6c404da151df170383c36e173e1ac

Aliases

arxiv: math/0607409 · arxiv_version: math/0607409v3 · doi: 10.48550/arxiv.math/0607409 · pith_short_12: 3ONB4G4SPR4R · pith_short_16: 3ONB4G4SPR4RVKUT · pith_short_8: 3ONB4G4S

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/3ONB4G4SPR4RVKUTP5OZPGJ2OD \
  | 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: db9a1e1b927c791aaa937f5d97993a70e1b6c404da151df170383c36e173e1ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e5eff12ccfa6268de9a83c6428a7e0c20c68c39d573467504d87d7fa2b25a02b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2006-07-18T06:06:10Z",
    "title_canon_sha256": "baf97ffa9fb168ea54ec76bcfed0c440be1e12e8e856df845b965e8b540bd155"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0607409",
    "kind": "arxiv",
    "version": 3
  }
}