Pith Number

pith:JZ7V73OC

pith:2010:JZ7V73OCWD22CBG3I6WLMPHXXK

not attested not anchored not stored refs pending

Inverse Additive Problems for Minkowski Sumsets II

D. J. Grynkiewicz, G. A. Freiman, O. Serra, Y. Stanchescu

arxiv:1012.3610 v1 · 2010-12-16 · math.NT · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JZ7V73OCWD22CBG3I6WLMPHXXK}

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	2026-05-18T03:07:02.427470Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e7f5fedc2b0f5a104db47acb63cf7ba864c4534b710b3d394dd4b83283c72fa

Aliases

arxiv: 1012.3610 · arxiv_version: 1012.3610v1 · doi: 10.48550/arxiv.1012.3610 · pith_short_12: JZ7V73OCWD22 · pith_short_16: JZ7V73OCWD22CBG3 · pith_short_8: JZ7V73OC

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/JZ7V73OCWD22CBG3I6WLMPHXXK \
  | 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: 4e7f5fedc2b0f5a104db47acb63cf7ba864c4534b710b3d394dd4b83283c72fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f8f3c8d522d3ab8cfff69f3a67988ef0fd25f672e6718833b99d7a02b8ea07d",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-12-16T14:13:09Z",
    "title_canon_sha256": "ca02b61afbc04f9685cd5f00bfb4eede715f8808683e15952d0a3d5e60ec69f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.3610",
    "kind": "arxiv",
    "version": 1
  }
}