Pith Number

pith:3LCRJB5K

pith:2011:3LCRJB5KJHTVAMXWB355KZRELI

not attested not anchored not stored refs pending

Stability for the multi-dimensional Borg-Levinson theorem with partial spectral data

Mourad Choulli, Plamen Stefanov

arxiv:1111.0231 v1 · 2011-11-01 · math.AP · 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{3LCRJB5KJHTVAMXWB355KZRELI}

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	2026-05-18T04:09:46.148942Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dac51487aa49e75032f60efbd566245a1dece9925385b9408dce0907492404a3

Aliases

arxiv: 1111.0231 · arxiv_version: 1111.0231v1 · doi: 10.48550/arxiv.1111.0231 · pith_short_12: 3LCRJB5KJHTV · pith_short_16: 3LCRJB5KJHTVAMXW · pith_short_8: 3LCRJB5K

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/3LCRJB5KJHTVAMXWB355KZRELI \
  | 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: dac51487aa49e75032f60efbd566245a1dece9925385b9408dce0907492404a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae9daa1a3f15d4e045d516d5e9e5054bf7354f6e9a2920014065e5f5ad512da0",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-11-01T16:08:37Z",
    "title_canon_sha256": "45d03feb1d74d2b633e4fa5b2733493259b294c7a00cc7ad98fb4428bf588ca0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.0231",
    "kind": "arxiv",
    "version": 1
  }
}