Pith Number

pith:CRTYBGVO

pith:2005:CRTYBGVOA5BOWZDSCG6XSPSC6D

not attested not anchored not stored refs pending

Spectral estimates for Schr\"odinger operator with periodic matrix potentials on the real line

Dmitri Chelkak, Evgeny Korotyaev

arxiv:math/0508568 v1 · 2005-08-29 · math.SP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CRTYBGVOA5BOWZDSCG6XSPSC6D}

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	2026-05-18T01:05:23.219895Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1467809aae0742eb647211bd793e42f0ebeae37ec985df028d92b0b01b0c4cd3

Aliases

arxiv: math/0508568 · arxiv_version: math/0508568v1 · doi: 10.48550/arxiv.math/0508568 · pith_short_12: CRTYBGVOA5BO · pith_short_16: CRTYBGVOA5BOWZDS · pith_short_8: CRTYBGVO

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/CRTYBGVOA5BOWZDSCG6XSPSC6D \
  | 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: 1467809aae0742eb647211bd793e42f0ebeae37ec985df028d92b0b01b0c4cd3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f9551b8126c2e60ca79c730884df6549f811199555ca24c0f5d5a0ba954ae8e",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.SP",
    "submitted_at": "2005-08-29T14:32:06Z",
    "title_canon_sha256": "4246e356648a3fef2f4bafdabbaa719c872c8f54683e17f79e527f70c5309b89"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0508568",
    "kind": "arxiv",
    "version": 1
  }
}