Pith Number

pith:AX4AYY4H

pith:2011:AX4AYY4HERC3JNSQOVL3GGN2EH

not attested not anchored not stored refs pending

Periodic Schr\"odinger operators with local defects and spectral pollution

Eric Canc\`es, Virginie Ehrlacher, Yvon Maday

arxiv:1111.3892 v1 · 2011-11-16 · 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{AX4AYY4HERC3JNSQOVL3GGN2EH}

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	2026-05-18T04:08:12.900097Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05f80c63872445b4b6507557b319ba21ca1aa89ca37c0dd47e53af1e632c127a

Aliases

arxiv: 1111.3892 · arxiv_version: 1111.3892v1 · doi: 10.48550/arxiv.1111.3892 · pith_short_12: AX4AYY4HERC3 · pith_short_16: AX4AYY4HERC3JNSQ · pith_short_8: AX4AYY4H

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/AX4AYY4HERC3JNSQOVL3GGN2EH \
  | 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: 05f80c63872445b4b6507557b319ba21ca1aa89ca37c0dd47e53af1e632c127a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3a07e513406820c4824ff9166e1871deab1fdc0d25cded42dfd87e06a844b82",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-11-16T18:03:25Z",
    "title_canon_sha256": "8c3a464f83b8425b03e338d420199d63c228567955020f342edd24f8153a32f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.3892",
    "kind": "arxiv",
    "version": 1
  }
}