Pith Number

pith:7IHON24Z

pith:2026:7IHON24ZAGPZEXOY43SJCKGNML

not attested not anchored not stored refs pending

Operator Learning for PDE Backstepping Control of Parabolic Equations on Time-Varying Domains

Jinrun Yan, Kai Liu, Zhong-Jie Han

arxiv:2606.17766 v1 · 2026-06-16 · math.OC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7IHON24ZAGPZEXOY43SJCKGNML}

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	2026-06-19T16:10:21.256475Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa0ee6eb99019f925dd8e6e49128cd62e86d10af8611498392580090fcf3201e

Aliases

arxiv: 2606.17766 · arxiv_version: 2606.17766v1 · doi: 10.48550/arxiv.2606.17766 · pith_short_12: 7IHON24ZAGPZ · pith_short_16: 7IHON24ZAGPZEXOY · pith_short_8: 7IHON24Z

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/7IHON24ZAGPZEXOY43SJCKGNML \
  | 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: fa0ee6eb99019f925dd8e6e49128cd62e86d10af8611498392580090fcf3201e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a043af7820453df3c6c3014cf2ac596fba10976c745f2e1f2d412dc5725e21f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-06-16T10:33:35Z",
    "title_canon_sha256": "ba99d5d8cf8134e66de7c32c2770e22dbbf8ea62bd1b112d0beb1cd96c8b72d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.17766",
    "kind": "arxiv",
    "version": 1
  }
}