Pith Number

pith:FPWBLA3D

pith:2021:FPWBLA3D4JETI76I6D4AWKVLJD

not attested not anchored not stored refs pending

The typical approximate structure of sets with bounded sumset

Marcelo Campos, Matthew Coulson, Maximilian W\"otzel, Oriol Serra

arxiv:2108.06253 v2 · 2021-08-13 · math.CO · math.NT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FPWBLA3D4JETI76I6D4AWKVLJD}

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	2026-07-05T05:36:45.050692Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2bec158363e249347fc8f0f80b2aab48ecf8cc9833051854f47ef19fd307665a

Aliases

arxiv: 2108.06253 · arxiv_version: 2108.06253v2 · doi: 10.48550/arxiv.2108.06253 · pith_short_12: FPWBLA3D4JET · pith_short_16: FPWBLA3D4JETI76I · pith_short_8: FPWBLA3D

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/FPWBLA3D4JETI76I6D4AWKVLJD \
  | 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: 2bec158363e249347fc8f0f80b2aab48ecf8cc9833051854f47ef19fd307665a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca420cdd3dcbdef6cf98fac66df385cc7796c9cb2b81b9654c6839ca412e8ef7",
    "cross_cats_sorted": [
      "math.NT",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-08-13T14:05:36Z",
    "title_canon_sha256": "31e09fdb3ba931c6483fb6c646f648425ecd280790cd3f9f5eecc026fec89b24"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2108.06253",
    "kind": "arxiv",
    "version": 2
  }
}