Pith Number

pith:TFCDBMM6

pith:2006:TFCDBMM6EUD3ARJVYXTJSFZQXC

not attested not anchored not stored refs pending

Density of non-residues in Burgess-type intervals and applications

D. R. Heath-Brown, I. E. Shparlinski, M. Z. Garaev, W. D. Banks

arxiv:math/0607692 v3 · 2006-07-27 · 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{TFCDBMM6EUD3ARJVYXTJSFZQXC}

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	2026-05-18T02:57:45.552746Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

994430b19e2507b04535c5e6991730b8bda2ce9931d9a3198ce4f5dbab668f23

Aliases

arxiv: math/0607692 · arxiv_version: math/0607692v3 · doi: 10.48550/arxiv.math/0607692 · pith_short_12: TFCDBMM6EUD3 · pith_short_16: TFCDBMM6EUD3ARJV · pith_short_8: TFCDBMM6

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/TFCDBMM6EUD3ARJVYXTJSFZQXC \
  | 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: 994430b19e2507b04535c5e6991730b8bda2ce9931d9a3198ce4f5dbab668f23

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3abca24f394abde4aa70e6bde5024ede0248d04a3dff4a2afbbe0e9f48465264",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2006-07-27T00:13:43Z",
    "title_canon_sha256": "64fbaf4fe87200eb72537acb857f49f3946bc9479090ade8a9f4d4b00ad0eb79"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0607692",
    "kind": "arxiv",
    "version": 3
  }
}