Pith Number

pith:A5BQBGG5

pith:2026:A5BQBGG55Y6VEGIVTG3BHSVKL2

not attested not anchored not stored refs pending

Backward Uniqueness for Coupled Ultraparabolic Operators and an Application to Jerk-Driven Control Models

Chao-Jiang Xu, Xiao-Dong Cao, Yan Xu

arxiv:2605.26993 v1 · 2026-05-26 · 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{A5BQBGG55Y6VEGIVTG3BHSVKL2}

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	2026-05-27T01:06:23.235147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

07430098ddee3d52191599b613caaa5e9e74548984c99ed7e315d4f7d28d7a54

Aliases

arxiv: 2605.26993 · arxiv_version: 2605.26993v1 · doi: 10.48550/arxiv.2605.26993 · pith_short_12: A5BQBGG55Y6V · pith_short_16: A5BQBGG55Y6VEGIV · pith_short_8: A5BQBGG5

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/A5BQBGG55Y6VEGIVTG3BHSVKL2 \
  | 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: 07430098ddee3d52191599b613caaa5e9e74548984c99ed7e315d4f7d28d7a54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1771fa4c1ffffc2618741e54dd1c4a423ea7753bc714be1edef63197e2536614",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-26T13:14:50Z",
    "title_canon_sha256": "c6367be7876aef801c87ebd19b22e21ec3cbbd4689b698ed29e06fdf42fe4ee8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.26993",
    "kind": "arxiv",
    "version": 1
  }
}