Pith Number

pith:TGOVCVHE

pith:2016:TGOVCVHEIUBPIBTFEXX34RQSXW

not attested not anchored not stored refs pending

Shadow lines in the arithmetic of elliptic curves

Bahare Mirza, Jaclyn Lang, Jennifer S. Balakrishnan, Mirela Ciperiani, Rachel Newton

arxiv:1610.08729 v1 · 2016-10-27 · 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{TGOVCVHEIUBPIBTFEXX34RQSXW}

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	2026-05-18T01:01:07.417773Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

999d5154e44502f4066525efbe4612bd89ef2a326e6cc3a2c43bd4407116b6f3

Aliases

arxiv: 1610.08729 · arxiv_version: 1610.08729v1 · doi: 10.48550/arxiv.1610.08729 · pith_short_12: TGOVCVHEIUBP · pith_short_16: TGOVCVHEIUBPIBTF · pith_short_8: TGOVCVHE

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/TGOVCVHEIUBPIBTFEXX34RQSXW \
  | 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: 999d5154e44502f4066525efbe4612bd89ef2a326e6cc3a2c43bd4407116b6f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b83eeaba8369081015a88cb1f4a1661066d606d1163c4ad8e3718fdbf8b2e4ed",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-10-27T12:03:13Z",
    "title_canon_sha256": "f42ebd859065350722de8c528888ba67dd03ebf98399c15bfcaaf20d8346e613"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.08729",
    "kind": "arxiv",
    "version": 1
  }
}