Pith Number

pith:MJD6XI4T

pith:2015:MJD6XI4T2DXYI25ZBK67CJOSF4

not attested not anchored not stored refs pending

Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three

Ciprian Demeter, Jean Bourgain, Larry Guth

arxiv:1512.01565 v3 · 2015-12-04 · 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{MJD6XI4T2DXYI25ZBK67CJOSF4}

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	2026-05-18T01:17:55.271624Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6247eba393d0ef846bb90abdf125d22f2d44b87a0ca6a3fd47646009a806a401

Aliases

arxiv: 1512.01565 · arxiv_version: 1512.01565v3 · doi: 10.48550/arxiv.1512.01565 · pith_short_12: MJD6XI4T2DXY · pith_short_16: MJD6XI4T2DXYI25Z · pith_short_8: MJD6XI4T

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/MJD6XI4T2DXYI25ZBK67CJOSF4 \
  | 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: 6247eba393d0ef846bb90abdf125d22f2d44b87a0ca6a3fd47646009a806a401

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66d22a1e657edc5a72cce076ba7a266833b1827aa6c49fd3e30d1c9a8bbfd706",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-12-04T21:09:37Z",
    "title_canon_sha256": "7978a64c06e2bba99b09abdcd4a480784a1ccc6061485ccd079c0d06f68760fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.01565",
    "kind": "arxiv",
    "version": 3
  }
}