Pith Number

pith:DRYPWMMM

pith:2025:DRYPWMMMJG52UYA3UOK474SNV7

not attested not anchored not stored refs pending

Control and its applications in additive combinatorics

Thomas F. Bloom

arxiv:2501.09470 v1 · 2025-01-16 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DRYPWMMMJG52UYA3UOK474SNV7}

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.

Cited by

3 papers in Pith

More sum-product type counterexamples: products with shifts and $AA+A$

Mathematical exploration and discovery at scale

A note on the sum-product problem for fractal sets

Receipt and verification

First computed	2026-07-05T10:01:47.561776Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c70fb318c49bbaa601ba395cff24dafd43b4aa7f6c28b47b9e5bbd5578f0605

Aliases

arxiv: 2501.09470 · arxiv_version: 2501.09470v1 · doi: 10.48550/arxiv.2501.09470 · pith_short_12: DRYPWMMMJG52 · pith_short_16: DRYPWMMMJG52UYA3 · pith_short_8: DRYPWMMM

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/DRYPWMMMJG52UYA3UOK474SNV7 \
  | 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: 1c70fb318c49bbaa601ba395cff24dafd43b4aa7f6c28b47b9e5bbd5578f0605

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e15c1eb73a189ee1cb1589ba574157650e89b945ab60a88e43be39da5c19630",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-01-16T11:15:08Z",
    "title_canon_sha256": "cbee4872daab055cc967be104f566a636353e0ef99f348a7073f7e07b14c2955"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.09470",
    "kind": "arxiv",
    "version": 1
  }
}