Pith Number

pith:6GOVPKKY

pith:2024:6GOVPKKYU32A5MPCEMRYVPHHIV

not attested not anchored not stored refs pending

Shadow line distributions

Barry Mazur, Jennifer S. Balakrishnan, Karl Rubin, Mirela \c{C}iperiani

arxiv:2409.00891 v2 · 2024-09-02 · 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{6GOVPKKYU32A5MPCEMRYVPHHIV}

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.

Cited by

1 paper in Pith

The density of elliptic curves over $\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny

Receipt and verification

First computed	2026-07-05T11:01:55.502336Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f19d57a958a6f40eb1e223238abce7457d27d7ab45d4f9174812ea73b0a3695f

Aliases

arxiv: 2409.00891 · arxiv_version: 2409.00891v2 · doi: 10.48550/arxiv.2409.00891 · pith_short_12: 6GOVPKKYU32A · pith_short_16: 6GOVPKKYU32A5MPC · pith_short_8: 6GOVPKKY

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/6GOVPKKYU32A5MPCEMRYVPHHIV \
  | 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: f19d57a958a6f40eb1e223238abce7457d27d7ab45d4f9174812ea73b0a3695f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d3afe9271060936e954245b2c099b7ac1a3b3e799b8ae21ec68a7b4ff0e4b710",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-09-02T02:00:12Z",
    "title_canon_sha256": "0a044c633b2fc6ebf51f360b2637a5ba3c831e4ed9370c4bc3b04ab6d05e78cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2409.00891",
    "kind": "arxiv",
    "version": 2
  }
}