Pith Number

pith:AFBHKTEX

pith:2015:AFBHKTEXOURYSTM7JYOCUW2YJK

not attested not anchored not stored refs pending

On pointwise estimates involving sparse operators

Andrei K. Lerner

arxiv:1512.07247 v1 · 2015-12-22 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AFBHKTEXOURYSTM7JYOCUW2YJK}

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	2026-05-18T01:13:04.778373Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0142754c977523894d9f4e1c2a5b584abf2f8bdfaabc31da437f1eb051f52639

Aliases

arxiv: 1512.07247 · arxiv_version: 1512.07247v1 · doi: 10.48550/arxiv.1512.07247 · pith_short_12: AFBHKTEXOURY · pith_short_16: AFBHKTEXOURYSTM7 · pith_short_8: AFBHKTEX

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/AFBHKTEXOURYSTM7JYOCUW2YJK \
  | 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: 0142754c977523894d9f4e1c2a5b584abf2f8bdfaabc31da437f1eb051f52639

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca2a731efa9008b45bf3807b32597804e675d4475b01fbc9fb0e2991ca332ace",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-12-22T20:52:47Z",
    "title_canon_sha256": "2fe51ad0193cc98eff58e2f2175b7af344f8ea780e7de7e558bac7c99d1188d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.07247",
    "kind": "arxiv",
    "version": 1
  }
}