Pith Number

pith:TIW72M3O

pith:2026:TIW72M3OTNOBZN4WR3VYZJ4TNK

not attested not anchored not stored refs pending

Quantum Communication Lower Bounds for Search Problems via Matrix Discrepancy

Chenghua Liu, Guangxu Yang, Minbo Gao, Tianyi Zhang

arxiv:2607.08517 v1 · 2026-07-09 · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TIW72M3OTNOBZN4WR3VYZJ4TNK}

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	2026-07-10T01:19:52.657945Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a2dfd336e9b5c1cb7968eeb8ca7936aa353e2756c2263659cc8651a7cabb9e2

Aliases

arxiv: 2607.08517 · arxiv_version: 2607.08517v1 · doi: 10.48550/arxiv.2607.08517 · pith_short_12: TIW72M3OTNOB · pith_short_16: TIW72M3OTNOBZN4W · pith_short_8: TIW72M3O

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/TIW72M3OTNOBZN4WR3VYZJ4TNK \
  | 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: 9a2dfd336e9b5c1cb7968eeb8ca7936aa353e2756c2263659cc8651a7cabb9e2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b2b40cb08cc1d34ab74ccf2936bbfd49aaa23642f3bb0393d34253ad2042633",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-07-09T14:11:09Z",
    "title_canon_sha256": "80933f49c75345bcfac8a0e71cc23f5ff3797b9e29ab5020376fefaace393024"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.08517",
    "kind": "arxiv",
    "version": 1
  }
}