Pith Number

pith:C5DB3LR3

pith:2011:C5DB3LR3AOQ7RPXL2POAQRTQUU

not attested not anchored not stored refs pending

The mixed boundary value problem, Krein resolvent formulas and spectral asymptotic estimates

Gerd Grubb

arxiv:1104.0785 v3 · 2011-04-05 · math.AP · 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{C5DB3LR3AOQ7RPXL2POAQRTQUU}

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	2026-05-18T04:18:04.039995Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

17461dae3b03a1f8beebd3dc084670a517b9d102cf6a09ded7708c5ec4c030a5

Aliases

arxiv: 1104.0785 · arxiv_version: 1104.0785v3 · doi: 10.48550/arxiv.1104.0785 · pith_short_12: C5DB3LR3AOQ7 · pith_short_16: C5DB3LR3AOQ7RPXL · pith_short_8: C5DB3LR3

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/C5DB3LR3AOQ7RPXL2POAQRTQUU \
  | 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: 17461dae3b03a1f8beebd3dc084670a517b9d102cf6a09ded7708c5ec4c030a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1b8d61320714ca91d88390108cfc6eda85d8094507c38a51641d4f97200ccd2",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-04-05T09:34:30Z",
    "title_canon_sha256": "2f0ec9462d8c94f8e0da5bacc7ab5c85985fb27b59f6279b9e38ec415585cb97"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.0785",
    "kind": "arxiv",
    "version": 3
  }
}