Pith Number

pith:T5KFP7KY

pith:2007:T5KFP7KYRIWXRYHYNVZIJLHGZI

not attested not anchored not stored refs pending

Vanishing and Non-Vanishing Dirichlet Twists of L-Functions of Elliptic Curves

Hershy Kisilevsky, Jack Fearnley, Masato Kuwata

arxiv:0711.1771 v3 · 2007-11-12 · 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{T5KFP7KYRIWXRYHYNVZIJLHGZI}

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	2026-05-18T02:58:12.093191Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f5457fd588a2d78e0f86d7284ace6ca23e6bfe8cf0f37f470a02f255f7919e4

Aliases

arxiv: 0711.1771 · arxiv_version: 0711.1771v3 · doi: 10.48550/arxiv.0711.1771 · pith_short_12: T5KFP7KYRIWX · pith_short_16: T5KFP7KYRIWXRYHY · pith_short_8: T5KFP7KY

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/T5KFP7KYRIWXRYHYNVZIJLHGZI \
  | 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: 9f5457fd588a2d78e0f86d7284ace6ca23e6bfe8cf0f37f470a02f255f7919e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90ae3e99ddfbd2c25fbd08232e1f911ce938b6a8f73cd342e9fb76fc05cc3343",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2007-11-12T13:39:40Z",
    "title_canon_sha256": "c6f7a1f5ec90378952886d6cdcc099426079000dc9b4685b83110ce97a6a2666"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0711.1771",
    "kind": "arxiv",
    "version": 3
  }
}