Pith Number

pith:WG3DNESM

pith:2026:WG3DNESMJUBKJYO7JFJPGAF76N

not attested not anchored not stored refs pending

Sharpness characterizes Hill functions

Marc Stephan

arxiv:2606.11426 v1 · 2026-06-09 · math.OC · math.CA · q-bio.QM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WG3DNESMJUBKJYO7JFJPGAF76N}

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	2026-06-11T01:09:48.019595Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1b636924c4d02a4e1df4952f300bff354538390db1a059e8e98fe82bde2045c

Aliases

arxiv: 2606.11426 · arxiv_version: 2606.11426v1 · doi: 10.48550/arxiv.2606.11426 · pith_short_12: WG3DNESMJUBK · pith_short_16: WG3DNESMJUBKJYO7 · pith_short_8: WG3DNESM

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/WG3DNESMJUBKJYO7JFJPGAF76N \
  | 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: b1b636924c4d02a4e1df4952f300bff354538390db1a059e8e98fe82bde2045c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23647dc2ff20db67d243f03dcbdba7c395f084cb71f261da6a18173a7932a6c5",
    "cross_cats_sorted": [
      "math.CA",
      "q-bio.QM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-06-09T20:23:20Z",
    "title_canon_sha256": "4e1b50743358bc51dc5be083eaf944ed473e9a9255ddfcf5d96894e381e77644"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.11426",
    "kind": "arxiv",
    "version": 1
  }
}