Pith Number

pith:HZ3NLV6K

pith:2015:HZ3NLV6KIJAMOSTHCTQRJP6ZIJ

not attested not anchored not stored refs pending

Shortest Distance in Modular Hyperbola and Least Quadratic Nonresidue

Tsz Ho Chan

arxiv:1509.07406 v1 · 2015-09-24 · 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{HZ3NLV6KIJAMOSTHCTQRJP6ZIJ}

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	2026-05-18T01:32:09.088718Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3e76d5d7ca4240c74a6714e114bfd9425e1c5db90a40784ea8e655279d790d97

Aliases

arxiv: 1509.07406 · arxiv_version: 1509.07406v1 · doi: 10.48550/arxiv.1509.07406 · pith_short_12: HZ3NLV6KIJAM · pith_short_16: HZ3NLV6KIJAMOSTH · pith_short_8: HZ3NLV6K

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/HZ3NLV6KIJAMOSTHCTQRJP6ZIJ \
  | 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: 3e76d5d7ca4240c74a6714e114bfd9425e1c5db90a40784ea8e655279d790d97

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "45bea42d39a694b6cc7d567bf979333b89fc4d0e0c5596b544d21a018e11b095",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-09-24T15:25:43Z",
    "title_canon_sha256": "1de377d4b1ea87eec57732434bbe0305d5745c138ef16f6932543cc7d7abd6f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.07406",
    "kind": "arxiv",
    "version": 1
  }
}