Pith Number

pith:HVGAHAPX

pith:2026:HVGAHAPXGCZFGX4P7QJXNPGA76

not attested not anchored not stored refs pending

Kardashev's Conundrum: Statistical Falsification of the Standard Kardashev Model and the Kardashev--Sagan--Nakamoto Resolution

Sebastian Gurovich

Global energy data falsifies the Kardashev 1% exponential model and requires renormalization by hashrate to restore physical coherence.

arxiv:2604.17516 v4 · 2026-04-19 · astro-ph.IM · astro-ph.GA

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\usepackage{pith}
\pithnumber{HVGAHAPXGCZFGX4P7QJXNPGA76}

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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.

Claims

C1strongest claim

No functional form fitted to P(t) alone can simultaneously satisfy statistical adequacy and physical coherence: the Kardashev variable is dimensionally incomplete. We propose the Kardashev-Sagan-Nakamoto (KSN) renormalisation B(t) = P(t)/H(t) [J/Hash, the KarNak unit].

C2weakest assumption

The linear model fitted to recent energy data will continue without bound or saturation long enough to reach solar luminosity levels, allowing the 1.6E15-year extrapolation to serve as a physical reductio.

C3one line summary

Statistical analysis of energy data falsifies the 1% exponential growth in the Kardashev model, shows linear extrapolation yields a 1.6E15-year Type II timescale, and introduces the KSN renormalization B(t) = P(t)/H(t) spanning 14 orders of magnitude.

Receipt and verification

First computed	2026-05-21T01:05:19.261346Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3d4c0381f730b2535f8ffc1376bcc0ff81cafd4acc64448f2c8bbef8a12bd900

Aliases

arxiv: 2604.17516 · arxiv_version: 2604.17516v4 · doi: 10.48550/arxiv.2604.17516 · pith_short_12: HVGAHAPXGCZF · pith_short_16: HVGAHAPXGCZFGX4P · pith_short_8: HVGAHAPX

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/HVGAHAPXGCZFGX4P7QJXNPGA76 \
  | 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: 3d4c0381f730b2535f8ffc1376bcc0ff81cafd4acc64448f2c8bbef8a12bd900

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aacb6cabcd3e53280770d3209a3ac3e1326385b30291a2b3572361e045865010",
    "cross_cats_sorted": [
      "astro-ph.GA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "astro-ph.IM",
    "submitted_at": "2026-04-19T16:19:28Z",
    "title_canon_sha256": "7723b92693f0a5af26ba9490082a66fe9cc78c0bcb2191dcf2101d9d0aa5ce00"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.17516",
    "kind": "arxiv",
    "version": 4
  }
}