Pith Number

pith:4RXXNJGQ

pith:2015:4RXXNJGQE4QRAALNBNBHSRGKZU

not attested not anchored not stored refs pending

Boundary controllability for a one-dimensional heat equation with a singular inverse-square potential

Umberto Biccari

arxiv:1509.05178 v3 · 2015-09-17 · 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{4RXXNJGQE4QRAALNBNBHSRGKZU}

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	2026-05-18T00:14:57.548429Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e46f76a4d0272110016d0b427944cacd3f6ea382c60a481df1b5cf68aa23d25c

Aliases

arxiv: 1509.05178 · arxiv_version: 1509.05178v3 · doi: 10.48550/arxiv.1509.05178 · pith_short_12: 4RXXNJGQE4QR · pith_short_16: 4RXXNJGQE4QRAALN · pith_short_8: 4RXXNJGQ

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/4RXXNJGQE4QRAALNBNBHSRGKZU \
  | 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: e46f76a4d0272110016d0b427944cacd3f6ea382c60a481df1b5cf68aa23d25c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df031de4079b51a38abb5edd646eb11222441d00e2d51020b5b6a249a0a3a896",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-09-17T09:33:19Z",
    "title_canon_sha256": "101776a1d44923ba1f45a8dfc863faeb66ded876073abc5c0aa307b08d096bbe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05178",
    "kind": "arxiv",
    "version": 3
  }
}