Pith Number

pith:ADYCLQGA

pith:2019:ADYCLQGA3BO3RO6VTFGOMCKZQD

not attested not anchored not stored refs pending

Double-phase problems and a discontinuity property of the spectrum

Du\v{s}an D. Repov\v{s}, Nikolaos S. Papageorgiou, Vicen\c{t}iu D. R\u{a}dulescu

arxiv:1906.01924 v2 · 2019-06-05 · 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{ADYCLQGA3BO3RO6VTFGOMCKZQD}

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	2026-05-17T23:39:35.249167Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00f025c0c0d85db8bbd5994ce6095980fe3af9cd3132b72f41574f2f2ea0becf

Aliases

arxiv: 1906.01924 · arxiv_version: 1906.01924v2 · doi: 10.48550/arxiv.1906.01924 · pith_short_12: ADYCLQGA3BO3 · pith_short_16: ADYCLQGA3BO3RO6V · pith_short_8: ADYCLQGA

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/ADYCLQGA3BO3RO6VTFGOMCKZQD \
  | 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: 00f025c0c0d85db8bbd5994ce6095980fe3af9cd3132b72f41574f2f2ea0becf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "108a98ebd5f111ae4de2a3ebbc9b65a6d69347c45c7851ea15a169caf08a7760",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-06-05T10:32:46Z",
    "title_canon_sha256": "e6efef4848d701b916b06528b82e58af4ade5048a84e7912d939038409cac7df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.01924",
    "kind": "arxiv",
    "version": 2
  }
}