Pith Number

pith:CBI3PDZ5

pith:2014:CBI3PDZ5OTITMF5EM25OIDIURM

not attested not anchored not stored refs pending

Minor arcs, mean values, and restriction theory for exponential sums over smooth numbers

Adam J. Harper

arxiv:1408.1662 v1 · 2014-08-07 · math.NT · math.CA · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CBI3PDZ5OTITMF5EM25OIDIURM}

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	2026-05-17T23:53:34.747466Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1051b78f3d74d13617a466bae40d148b3f6977589f7ef51339c73deac51001a6

Aliases

arxiv: 1408.1662 · arxiv_version: 1408.1662v1 · doi: 10.48550/arxiv.1408.1662 · pith_short_12: CBI3PDZ5OTIT · pith_short_16: CBI3PDZ5OTITMF5E · pith_short_8: CBI3PDZ5

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/CBI3PDZ5OTITMF5EM25OIDIURM \
  | 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: 1051b78f3d74d13617a466bae40d148b3f6977589f7ef51339c73deac51001a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a9cf4fb1a29fcda4d533ce69efa4154fbb6393b69017b8dfdab96e6242f9fb9",
    "cross_cats_sorted": [
      "math.CA",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-08-07T17:32:35Z",
    "title_canon_sha256": "85007d592b95c4496c9a793d1e18452fd203d4bbccd5463dfc16e54d7be0679f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.1662",
    "kind": "arxiv",
    "version": 1
  }
}