Pith Number

pith:Z3JAEPPZ

pith:2007:Z3JAEPPZ7YLUCJ34G2BP3PBQRK

not attested not anchored not stored refs pending

Absolute Continuity of the Integrated Density of States for the Almost Mathieu Operator with Non-Critical Coupling

Artur Avila, David Damanik

arxiv:0711.4291 v1 · 2007-11-27 · math.DS · math-ph · math.MP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z3JAEPPZ7YLUCJ34G2BP3PBQRK}

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	2026-05-18T02:26:39.781890Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ced2023df9fe1741277c3682fdbc308ab21f4948e770b601457284180c383ba4

Aliases

arxiv: 0711.4291 · arxiv_version: 0711.4291v1 · doi: 10.48550/arxiv.0711.4291 · pith_short_12: Z3JAEPPZ7YLU · pith_short_16: Z3JAEPPZ7YLUCJ34 · pith_short_8: Z3JAEPPZ

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/Z3JAEPPZ7YLUCJ34G2BP3PBQRK \
  | 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: ced2023df9fe1741277c3682fdbc308ab21f4948e770b601457284180c383ba4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8627685584f6f0f27a8c3fc96b8d181b8d713db396d699a48430d915cc8595a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2007-11-27T16:08:40Z",
    "title_canon_sha256": "baad49e2a84ecdca8beb63417ac3b97919c44794401c77c7265cc75b46b353be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0711.4291",
    "kind": "arxiv",
    "version": 1
  }
}