Pith Number

pith:BEUTUBEC

pith:2017:BEUTUBECRMHUE53WCHXZ5IY3F5

not attested not anchored not stored refs pending

A note on Linnik's Theorem on quadratic non-residues

B\'ela Bollob\'as, Jonathan D. Lee, Oliver Riordan, Paul Balister, Robert Morris

arxiv:1712.07179 v1 · 2017-12-19 · 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{BEUTUBECRMHUE53WCHXZ5IY3F5}

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	2026-05-18T00:27:35.346725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09293a04828b0f42777611ef9ea31b2f4a460c6697203ecc4074d782c97a0d4a

Aliases

arxiv: 1712.07179 · arxiv_version: 1712.07179v1 · doi: 10.48550/arxiv.1712.07179 · pith_short_12: BEUTUBECRMHU · pith_short_16: BEUTUBECRMHUE53W · pith_short_8: BEUTUBEC

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/BEUTUBECRMHUE53WCHXZ5IY3F5 \
  | 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: 09293a04828b0f42777611ef9ea31b2f4a460c6697203ecc4074d782c97a0d4a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3dfadc9dcd3dfa0fe41100f33a492ab68461e0eaa629c4d6be2877adac3438d",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-12-19T19:53:12Z",
    "title_canon_sha256": "9a4ce895384a56309a28a7cd148330f3883958c3bc71f8798c377ad149836eef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.07179",
    "kind": "arxiv",
    "version": 1
  }
}