Pith Number

pith:TYZNYHQX

pith:2018:TYZNYHQXCLXPEHYMQXIACDSYIP

not attested not anchored not stored refs pending

Trace class perturbation of closed linear relations

Yan Liu, Yuming Shi

arxiv:1812.02324 v1 · 2018-12-06 · 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{TYZNYHQXCLXPEHYMQXIACDSYIP}

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	2026-05-17T23:58:56.582431Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e32dc1e1712eef21f0c85d0010e5843e30d046cbd42fde949c0a1e2f306d9a1

Aliases

arxiv: 1812.02324 · arxiv_version: 1812.02324v1 · doi: 10.48550/arxiv.1812.02324 · pith_short_12: TYZNYHQXCLXP · pith_short_16: TYZNYHQXCLXPEHYM · pith_short_8: TYZNYHQX

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/TYZNYHQXCLXPEHYMQXIACDSYIP \
  | 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: 9e32dc1e1712eef21f0c85d0010e5843e30d046cbd42fde949c0a1e2f306d9a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ec078610129fbbf150c58ccf27efb5b6f86c9a0e62cee9c04baefec541ccd68",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2018-12-06T03:02:40Z",
    "title_canon_sha256": "d244c54147bcbdd41504faa5ce16cc733843ad4ad05809de3b6a0d6f35e636fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.02324",
    "kind": "arxiv",
    "version": 1
  }
}