Pith Number

pith:PNZDIDLE

pith:2017:PNZDIDLEHKJXKOG7BFS6KFVBU5

not attested not anchored not stored refs pending

Gradient of eigenvalues of Dirac operators and its applications

Tigran Harutyunyan, Yuri Ashrafyan

arxiv:1705.02306 v1 · 2017-05-05 · math.CA · 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{PNZDIDLEHKJXKOG7BFS6KFVBU5}

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	2026-05-18T00:44:58.626384Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b72340d643a937538df0965e516a1a746661823101bd8072104202cf40d8c9d

Aliases

arxiv: 1705.02306 · arxiv_version: 1705.02306v1 · doi: 10.48550/arxiv.1705.02306 · pith_short_12: PNZDIDLEHKJX · pith_short_16: PNZDIDLEHKJXKOG7 · pith_short_8: PNZDIDLE

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/PNZDIDLEHKJXKOG7BFS6KFVBU5 \
  | 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: 7b72340d643a937538df0965e516a1a746661823101bd8072104202cf40d8c9d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c174722f0cd990224f4d324d173c787a2ec4f194f4bae986f4068b21fe4a72aa",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-05-05T17:17:32Z",
    "title_canon_sha256": "90ffeafe0041a7e4feda30eb41dad542c8281734b97ceeadb26568b6ecd80f13"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.02306",
    "kind": "arxiv",
    "version": 1
  }
}