Pith Number

pith:HUT4JEL2

pith:2018:HUT4JEL2Q4X6XHJX4CBI6TPRCX

not attested not anchored not stored refs pending

Relative Morse index theory and applications in wave equations

L.Wu, Q.Wang

arxiv:1810.07933 v1 · 2018-10-18 · 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{HUT4JEL2Q4X6XHJX4CBI6TPRCX}

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	2026-05-18T00:02:53.706795Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3d27c4917a872feb9d37e0828f4df115dea9f0903b927f043eed577b922b8d0b

Aliases

arxiv: 1810.07933 · arxiv_version: 1810.07933v1 · doi: 10.48550/arxiv.1810.07933 · pith_short_12: HUT4JEL2Q4X6 · pith_short_16: HUT4JEL2Q4X6XHJX · pith_short_8: HUT4JEL2

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/HUT4JEL2Q4X6XHJX4CBI6TPRCX \
  | 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: 3d27c4917a872feb9d37e0828f4df115dea9f0903b927f043eed577b922b8d0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10491f046601056ff8075b3848f1a169a1dfe96b83fe058dd41b96a62637b7b1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-10-18T07:46:42Z",
    "title_canon_sha256": "08ee3e5317e8ae6ef4c8e7f83d9b57ace687c84cceda8f839bf7f304b9271c19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.07933",
    "kind": "arxiv",
    "version": 1
  }
}