Pith Number

pith:2O3FMYKE

pith:2014:2O3FMYKE5HNOC5GGN2JPO3EXLM

not attested not anchored not stored refs pending

The distribution of values of short hybrid exponential sums on curves over finite fields II

Kit-Ho Mak

arxiv:1408.1244 v1 · 2014-08-06 · 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{2O3FMYKE5HNOC5GGN2JPO3EXLM}

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	2026-05-18T02:45:47.845376Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3b6566144e9dae174c66e92f76c975b0c464a3eedcca4e4e25f4ccd3ea3a420

Aliases

arxiv: 1408.1244 · arxiv_version: 1408.1244v1 · doi: 10.48550/arxiv.1408.1244 · pith_short_12: 2O3FMYKE5HNO · pith_short_16: 2O3FMYKE5HNOC5GG · pith_short_8: 2O3FMYKE

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/2O3FMYKE5HNOC5GGN2JPO3EXLM \
  | 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: d3b6566144e9dae174c66e92f76c975b0c464a3eedcca4e4e25f4ccd3ea3a420

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "646ae31e36c45560f289e116e29c8a17e87a2d77db48b6fd0c31a50ebca33b22",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-08-06T11:02:54Z",
    "title_canon_sha256": "c670e17353e0f20d4b7de5b8ca637c012e66bf5cbc6d4724d8cef5f63f314f39"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.1244",
    "kind": "arxiv",
    "version": 1
  }
}