Pith Number

pith:DS4IF3A4

pith:2026:DS4IF3A45CYGWPP6EKLGJ3BBC2

not attested not anchored not stored refs pending

Controllable subspaces and real-part observability for Schr\"odinger equations on $\mathbb T^d$

Gengsheng Wang, Ming Wang

arxiv:2608.04357 v1 · 2026-08-05 · math.AP · 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{DS4IF3A45CYGWPP6EKLGJ3BBC2}

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	2026-08-06T01:33:36.511443Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1cb882ec1ce8b06b3dfe229664ec21169d0fccf48d42104039f5e0bc842ba5b1

Aliases

arxiv: 2608.04357 · arxiv_version: 2608.04357v1 · doi: 10.48550/arxiv.2608.04357 · pith_short_12: DS4IF3A45CYG · pith_short_16: DS4IF3A45CYGWPP6 · pith_short_8: DS4IF3A4

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/DS4IF3A45CYGWPP6EKLGJ3BBC2 \
  | 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: 1cb882ec1ce8b06b3dfe229664ec21169d0fccf48d42104039f5e0bc842ba5b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "25186e3bf5d82ef5be7c36c08f256191a2fe94ea94267e48f795ddc2acf2f564",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-08-05T01:56:32Z",
    "title_canon_sha256": "a5758654ef230120010724c872243b99e20a2b7fe71b5adba44e9c035603c79f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.04357",
    "kind": "arxiv",
    "version": 1
  }
}