Pith Number

pith:VFDD5UDY

pith:2005:VFDD5UDYP4X5KJY3CK2NDDGYQM

not attested not anchored not stored refs pending

On the logarithmic factor in error term estimates in certain additive congruence problems

M. Z. Garaev

arxiv:math/0504280 v1 · 2005-04-13 · 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{VFDD5UDYP4X5KJY3CK2NDDGYQM}

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	2026-05-18T01:38:26.829955Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9463ed0787f2fd5271b12b4d18cd88315db1dbe5230b598be21584c37d966c6

Aliases

arxiv: math/0504280 · arxiv_version: math/0504280v1 · doi: 10.48550/arxiv.math/0504280 · pith_short_12: VFDD5UDYP4X5 · pith_short_16: VFDD5UDYP4X5KJY3 · pith_short_8: VFDD5UDY

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/VFDD5UDYP4X5KJY3CK2NDDGYQM \
  | 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: a9463ed0787f2fd5271b12b4d18cd88315db1dbe5230b598be21584c37d966c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11b6a9e0c458021c92568bad9128eb1ad4933e2e2cd0bfb440ed9ed6f88e472e",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2005-04-13T19:14:47Z",
    "title_canon_sha256": "3e5e00e770390c6b037143f10765c2f8ef566f1fc2a93c3c4c88affb8de04e73"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0504280",
    "kind": "arxiv",
    "version": 1
  }
}