Pith Number

pith:VBVCKEZT

pith:2026:VBVCKEZTZ3YRTJPEEPDESPVPVK

not attested not anchored not stored refs pending

Improved Bounds for Distinct Multiples in Intervals

Kaizhe Chen

arxiv:2607.26450 v1 · 2026-07-29 · math.NT · 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{VBVCKEZTZ3YRTJPEEPDESPVPVK}

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	2026-07-30T01:20:32.268506Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

a86a251333cef119a5e423c6493eafaa91ecffae84d47f6a2b02a3dc89265528

Aliases

arxiv: 2607.26450 · arxiv_version: 2607.26450v1 · doi: 10.48550/arxiv.2607.26450 · pith_short_12: VBVCKEZTZ3YR · pith_short_16: VBVCKEZTZ3YRTJPE · pith_short_8: VBVCKEZT

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/VBVCKEZTZ3YRTJPEEPDESPVPVK \
  | 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: a86a251333cef119a5e423c6493eafaa91ecffae84d47f6a2b02a3dc89265528

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be26ad790cb7bab201f942383e16f99366e93a37d064cb4e57ace5580473b7bf",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-29T04:03:50Z",
    "title_canon_sha256": "71edca6a9defa578c0621f26d5a024abb402ec1933cd6e11f10eea239e402cdf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.26450",
    "kind": "arxiv",
    "version": 1
  }
}