Pith Number

pith:5PDKFDE5

pith:2026:5PDKFDE5JPPGR3LBONADGBWBYT

not attested not anchored not stored refs pending

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes

Manuel C\'aceres, Saeed Odak, S\'andor Kisfaludi-Bak

arxiv:2607.06069 v1 · 2026-07-07 · cs.CG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5PDKFDE5JPPGR3LBONADGBWBYT}

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	2026-07-08T01:18:55.526377Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebc6a28c9d4bde68ed6173403306c1c4caf559d8fede87fdef34a3beca53eef0

Aliases

arxiv: 2607.06069 · arxiv_version: 2607.06069v1 · doi: 10.48550/arxiv.2607.06069 · pith_short_12: 5PDKFDE5JPPG · pith_short_16: 5PDKFDE5JPPGR3LB · pith_short_8: 5PDKFDE5

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/5PDKFDE5JPPGR3LBONADGBWBYT \
  | 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: ebc6a28c9d4bde68ed6173403306c1c4caf559d8fede87fdef34a3beca53eef0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20d839340a0e4138eaaedf178b4fc40eedcef4e9f19c536969d01d3e686607cb",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CG",
    "submitted_at": "2026-07-07T09:40:33Z",
    "title_canon_sha256": "843c404579d3f6abee5db3f42a89a6942aa84da803857fe403597b7c511db787"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.06069",
    "kind": "arxiv",
    "version": 1
  }
}