Pith Number

pith:JENVRTHT

pith:2019:JENVRTHTW24WHDTBDZZ22WGPL2

not attested not anchored not stored refs pending

Decoupling theorems for the Duffin-Schaeffer problem

Christoph Aistleitner

arxiv:1907.04590 v1 · 2019-07-10 · 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{JENVRTHTW24WHDTBDZZ22WGPL2}

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	2026-05-17T23:40:59.780787Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

491b58ccf3b6b9638e611e73ad58cf5ea2945e5cc5a0c25a0be78ff5a162795c

Aliases

arxiv: 1907.04590 · arxiv_version: 1907.04590v1 · doi: 10.48550/arxiv.1907.04590 · pith_short_12: JENVRTHTW24W · pith_short_16: JENVRTHTW24WHDTB · pith_short_8: JENVRTHT

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/JENVRTHTW24WHDTBDZZ22WGPL2 \
  | 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: 491b58ccf3b6b9638e611e73ad58cf5ea2945e5cc5a0c25a0be78ff5a162795c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8952889ed8e4cf40d384c30ff949383e1abe647f9b6a19e102125ed363eb3137",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-07-10T09:37:00Z",
    "title_canon_sha256": "75d72a11108efa3b899a5d6f034ba987c2cb1841ce6af4ee87fb0326a34a66c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.04590",
    "kind": "arxiv",
    "version": 1
  }
}