Pith Number

pith:C5S7KKD2

pith:2013:C5S7KKD2HUG7FTFA65WNZYFLMB

not attested not anchored not stored refs pending

Lower bounds for the counting function of integral operators

Yuri Safarov

arxiv:1308.4078 v1 · 2013-08-19 · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C5S7KKD2HUG7FTFA65WNZYFLMB}

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	2026-05-18T03:15:34.922106Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1765f5287a3d0df2cca0f76cdce0ab607187920d41d204a076e5464f3d8d6858

Aliases

arxiv: 1308.4078 · arxiv_version: 1308.4078v1 · doi: 10.48550/arxiv.1308.4078 · pith_short_12: C5S7KKD2HUG7 · pith_short_16: C5S7KKD2HUG7FTFA · pith_short_8: C5S7KKD2

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/C5S7KKD2HUG7FTFA65WNZYFLMB \
  | 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: 1765f5287a3d0df2cca0f76cdce0ab607187920d41d204a076e5464f3d8d6858

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ecdfc5c63666f1ffa07c4f8280a11c175bc6ec4530d6ed64cc4a05cffd6a8ca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2013-08-19T17:21:05Z",
    "title_canon_sha256": "be1d67e19f6ebd9826b8392bbf48289b73c75c7424f833057700d3d79e897a16"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.4078",
    "kind": "arxiv",
    "version": 1
  }
}