Pith Number

pith:KRT2K3RR

pith:2026:KRT2K3RRGK3XQ3RKFLS63KOG7H

not attested not anchored not stored refs pending

Sharp bounds between the saturation number and the harmonic index

Chakshu Gupta

arxiv:2606.15761 v3 · 2026-06-14 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KRT2K3RRGK3XQ3RKFLS63KOG7H}

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	2026-06-19T16:12:56.071099Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5467a56e3132b7786e2a2ae5eda9c6f9caa49bb6b280778bed3d0cce5e5403f8

Aliases

arxiv: 2606.15761 · arxiv_version: 2606.15761v3 · doi: 10.48550/arxiv.2606.15761 · pith_short_12: KRT2K3RRGK3X · pith_short_16: KRT2K3RRGK3XQ3RK · pith_short_8: KRT2K3RR

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/KRT2K3RRGK3XQ3RKFLS63KOG7H \
  | 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: 5467a56e3132b7786e2a2ae5eda9c6f9caa49bb6b280778bed3d0cce5e5403f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74ee201b93e7bff34aa076b5b731a4b528616d81407167a1a31df4312408203f",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-14T11:46:02Z",
    "title_canon_sha256": "56cfb7ac063a21f912ce1bfc4060c9e83f0b3abd88b87fb36ae973734d9d969d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.15761",
    "kind": "arxiv",
    "version": 3
  }
}