Pith Number

pith:JABUU4K3

pith:2026:JABUU4K3LXHSAZ3YC4QR5OGKFT

not attested not anchored not stored refs pending

Double-Exponential Quasi-Orthogonality: The Geometry of Decoherence

Karl Svozil

In high-dimensional Hilbert spaces almost all state vectors are nearly orthogonal, supplying an exponentially large reservoir of mutually quasi-orthogonal environmental records that prevents visible interference between macroscopic quantum

arxiv:2605.03807 v2 · 2026-05-05 · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JABUU4K3LXHSAZ3YC4QR5OGKFT}

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.

Claims

C1strongest claim

In a high-dimensional Hilbert space, almost all state vectors are nearly orthogonal, accommodating an exponentially large reservoir of mutually quasi-orthogonal environmental records. This geometry explains why macroscopic alternatives fail to exhibit visible interference once such records are populated.

C2weakest assumption

That the system's Hamiltonian and the environment's degrees of freedom will actually populate these typical quasi-orthogonal records rather than atypical ones; the paper explicitly notes that geometry alone does not guarantee the dynamics drive the system into the typical region of the accessible subspace.

C3one line summary

In high-dimensional Hilbert spaces, near-orthogonality of almost all vectors supplies an exponentially large reservoir of mutually quasi-orthogonal environmental records that makes decoherence overwhelmingly effective for macroscopic systems.

Receipt and verification

First computed	2026-07-14T01:21:00.401971Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

48034a715b5dcf20677817211eb8ca2ceb943145471eb7efbad2ad3e7d1809ea

Aliases

arxiv: 2605.03807 · arxiv_version: 2605.03807v2 · doi: 10.48550/arxiv.2605.03807 · pith_short_12: JABUU4K3LXHS · pith_short_16: JABUU4K3LXHSAZ3Y · pith_short_8: JABUU4K3

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/JABUU4K3LXHSAZ3YC4QR5OGKFT \
  | 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: 48034a715b5dcf20677817211eb8ca2ceb943145471eb7efbad2ad3e7d1809ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "57136ed0fed592b474ed6d180d23bf54b2ad400b45fc639f8501ff9660506fe8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-05T14:31:58Z",
    "title_canon_sha256": "51d014b09ee403dce5c4c7e79fafcff03aecae3b11f917b75276004edbea5e12"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.03807",
    "kind": "arxiv",
    "version": 2
  }
}