Pith Number

pith:2VXPKDEP

pith:2025:2VXPKDEPMATM7KN32IUSXYDSTL

not attested not anchored not stored refs pending

Additive structure in convex sets

Jakob F\"uhrer, Oliver Roche-Newton, Thomas F. Bloom

arxiv:2509.01568 v1 · 2025-09-01 · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2VXPKDEPMATM7KN32IUSXYDSTL}

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	2026-07-05T12:03:03.383117Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d56ef50c8f6026cfa9bbd2292be0729ac72b817ca0bac3ab1a9f00c1c4da608c

Aliases

arxiv: 2509.01568 · arxiv_version: 2509.01568v1 · doi: 10.48550/arxiv.2509.01568 · pith_short_12: 2VXPKDEPMATM · pith_short_16: 2VXPKDEPMATM7KN3 · pith_short_8: 2VXPKDEP

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/2VXPKDEPMATM7KN32IUSXYDSTL \
  | 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: d56ef50c8f6026cfa9bbd2292be0729ac72b817ca0bac3ab1a9f00c1c4da608c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8342a5947d0ea3a11da0a6c3d781f757801b8f6cb107607f4c9a8cd2b9da0d3c",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-09-01T15:52:59Z",
    "title_canon_sha256": "ff028127c5fb4cbb131e5e6a249c1a7292174edc908ac309c6d924be3798029c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.01568",
    "kind": "arxiv",
    "version": 1
  }
}