Pith Number

pith:ENJNKRQD

pith:2006:ENJNKRQDEWOC2OBOPP7XCOW7UQ

not attested not anchored not stored refs pending

Explicit n-descent on elliptic curves, I. Algebra

Cathy O'Neil, Denis Simon, John Cremona, Michael Stoll, Tom Fisher

arxiv:math/0606580 v1 · 2006-06-23 · 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{ENJNKRQDEWOC2OBOPP7XCOW7UQ}

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	2026-05-18T01:10:00.370517Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2352d54603259c2d382e7bff713adfa404c4c14a95472d59a976814bb23718f2

Aliases

arxiv: math/0606580 · arxiv_version: math/0606580v1 · doi: 10.48550/arxiv.math/0606580 · pith_short_12: ENJNKRQDEWOC · pith_short_16: ENJNKRQDEWOC2OBO · pith_short_8: ENJNKRQD

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/ENJNKRQDEWOC2OBOPP7XCOW7UQ \
  | 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: 2352d54603259c2d382e7bff713adfa404c4c14a95472d59a976814bb23718f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "febfd68c19fc013a50e129b27b1499ceb29d93314eb0e277428c2bea4df4a640",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2006-06-23T08:29:03Z",
    "title_canon_sha256": "fa4fc3c8cc7257a0fb6fe9b63c102a251dcdd2a578955ffd7f5d58cff333c843"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0606580",
    "kind": "arxiv",
    "version": 1
  }
}