Pith Number

pith:KPBR2POP

pith:2011:KPBR2POPZ2KG7TGE7X7D7QYJHP

not attested not anchored not stored refs pending

Refinements of Miller's Algorithm over Weierstrass Curves Revisited

Chao-Liang Liu, Duc-Phong Le

arxiv:1103.0337 v1 · 2011-03-02 · cs.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KPBR2POPZ2KG7TGE7X7D7QYJHP}

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	2026-05-18T04:27:35.211326Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53c31d3dcfce946fccc4fdfe3fc3093bdeb8a94ca183a1120c27eef2ad59d2f8

Aliases

arxiv: 1103.0337 · arxiv_version: 1103.0337v1 · doi: 10.48550/arxiv.1103.0337 · pith_short_12: KPBR2POPZ2KG · pith_short_16: KPBR2POPZ2KG7TGE · pith_short_8: KPBR2POP

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/KPBR2POPZ2KG7TGE7X7D7QYJHP \
  | 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: 53c31d3dcfce946fccc4fdfe3fc3093bdeb8a94ca183a1120c27eef2ad59d2f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d55a3e03aaa976012a343ac87684f787b61e3ce4344862efa2046041103485b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2011-03-02T02:50:33Z",
    "title_canon_sha256": "d46fb2f3c755505ddcc3994dff65bd2a62f9f6d20a48bef06f8aa02648056b8b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.0337",
    "kind": "arxiv",
    "version": 1
  }
}