Pith Number

pith:3QL4IMYL

pith:2002:3QL4IMYLU2BBZR4BBOK6XCPSSV

not attested not anchored not stored refs pending

On the distribution of the of Frobenius elements on elliptic curves over function fields

Amilcar Pacheco

arxiv:math/0211315 v1 · 2002-11-20 · math.NT · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3QL4IMYLU2BBZR4BBOK6XCPSSV}

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	2026-05-18T01:38:29.325238Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc17c4330ba6821cc7810b95eb89f2957a71057e060d6817c07c21183274ff27

Aliases

arxiv: math/0211315 · arxiv_version: math/0211315v1 · doi: 10.48550/arxiv.math/0211315 · pith_short_12: 3QL4IMYLU2BB · pith_short_16: 3QL4IMYLU2BBZR4B · pith_short_8: 3QL4IMYL

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/3QL4IMYLU2BBZR4BBOK6XCPSSV \
  | 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: dc17c4330ba6821cc7810b95eb89f2957a71057e060d6817c07c21183274ff27

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad444560265d6696eac77b03a029960c4915a2212a38fb8f49ec3cf376d91300",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2002-11-20T11:23:51Z",
    "title_canon_sha256": "dff2e3c0c506140b671aac756624eb9b5042cf366cc06ac3d199a75146465be9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0211315",
    "kind": "arxiv",
    "version": 1
  }
}