Pith Number

pith:MBCVMHAW

pith:2017:MBCVMHAWQ77DFVHYIO7QM5UGNR

not attested not anchored not stored refs pending

Incidence Results and Bounds of Trilinear and Quadrilinear Exponential Sums

Simon Macourt

arxiv:1707.08268 v2 · 2017-07-26 · 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{MBCVMHAWQ77DFVHYIO7QM5UGNR}

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	2026-05-18T00:36:19.035112Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6045561c1687fe32d4f843bf0676866c5377d278751a0cba0f55617c57caeca2

Aliases

arxiv: 1707.08268 · arxiv_version: 1707.08268v2 · doi: 10.48550/arxiv.1707.08268 · pith_short_12: MBCVMHAWQ77D · pith_short_16: MBCVMHAWQ77DFVHY · pith_short_8: MBCVMHAW

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/MBCVMHAWQ77DFVHYIO7QM5UGNR \
  | 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: 6045561c1687fe32d4f843bf0676866c5377d278751a0cba0f55617c57caeca2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82711e2c4bab8d1b9e04a81494732062495ab70c5297edfbec463f8200d90819",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-07-26T01:32:33Z",
    "title_canon_sha256": "dddf9615cada2dde286999b42b696d1c733cbd64cadc72ecbdb759d4b108875a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.08268",
    "kind": "arxiv",
    "version": 2
  }
}