Pith Number

pith:ZKBGXMTN

pith:2018:ZKBGXMTNZ7H4TO4Y2WLHP6C3EO

not attested not anchored not stored refs pending

Asymptotics of Goldbach Representations

Gautami Bhowmik, Karin Halupczok

arxiv:1809.06920 v2 · 2018-09-18 · 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{ZKBGXMTNZ7H4TO4Y2WLHP6C3EO}

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	2026-05-18T00:03:55.348027Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca826bb26dcfcfc9bb98d59677f85b23947b67fb156c7b82e4943b319cecfe50

Aliases

arxiv: 1809.06920 · arxiv_version: 1809.06920v2 · doi: 10.48550/arxiv.1809.06920 · pith_short_12: ZKBGXMTNZ7H4 · pith_short_16: ZKBGXMTNZ7H4TO4Y · pith_short_8: ZKBGXMTN

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/ZKBGXMTNZ7H4TO4Y2WLHP6C3EO \
  | 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: ca826bb26dcfcfc9bb98d59677f85b23947b67fb156c7b82e4943b319cecfe50

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "796918686a013d7331431046a452e437d169b6c592b2fe6ae938736cf3f36e5e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-09-18T20:25:39Z",
    "title_canon_sha256": "ce836008f994f99561baa15fefa5d85747a9bc0a03f7082c3ebee0150301da09"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.06920",
    "kind": "arxiv",
    "version": 2
  }
}