Pith Number

pith:Z7D3GRBU

pith:2012:Z7D3GRBUXJBMJWPH4R4DIHZFYK

not attested not anchored not stored refs pending

Exact multiplicity results for a singularly perturbed Neumann problem

Massimo Grossi, S\'ergio Neves

arxiv:1211.0569 v1 · 2012-11-02 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z7D3GRBUXJBMJWPH4R4DIHZFYK}

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	2026-05-18T03:41:33.071672Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfc7b34434ba42c4d9e7e478341f25c2b7ee90139f24d1f5a25a1cd3608754fd

Aliases

arxiv: 1211.0569 · arxiv_version: 1211.0569v1 · doi: 10.48550/arxiv.1211.0569 · pith_short_12: Z7D3GRBUXJBM · pith_short_16: Z7D3GRBUXJBMJWPH · pith_short_8: Z7D3GRBU

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/Z7D3GRBUXJBMJWPH4R4DIHZFYK \
  | 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: cfc7b34434ba42c4d9e7e478341f25c2b7ee90139f24d1f5a25a1cd3608754fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e845f5971deaf9d3d8e762dca6fa32fcf93d37f681f039b69eb2f7810086369f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-11-02T21:49:21Z",
    "title_canon_sha256": "09043607694a070509c447d928ba12aeca30e1bb5271a96c5ea08c3f19d7bb92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.0569",
    "kind": "arxiv",
    "version": 1
  }
}