Pith Number

pith:MVUZINXP

pith:2017:MVUZINXP4EKOEHGNXV6PALAUW2

not attested not anchored not stored refs pending

Spectral gaps for the Two-Species Product Vacua and Boundary States models on the $d$-dimensional lattice

Michael Bishop

arxiv:1705.04755 v2 · 2017-05-12 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MVUZINXP4EKOEHGNXV6PALAUW2}

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	2026-05-18T00:21:28.105350Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65699436efe114e21ccdbd7cf02c14b6b5d206266c44f10f93c021583d7aa197

Aliases

arxiv: 1705.04755 · arxiv_version: 1705.04755v2 · doi: 10.48550/arxiv.1705.04755 · pith_short_12: MVUZINXP4EKO · pith_short_16: MVUZINXP4EKOEHGN · pith_short_8: MVUZINXP

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/MVUZINXP4EKOEHGNXV6PALAUW2 \
  | 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: 65699436efe114e21ccdbd7cf02c14b6b5d206266c44f10f93c021583d7aa197

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "32f30456a2f8e581eecc16426efcf3e3236632ab21bce8c78b63beecb8192c8c",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2017-05-12T21:31:27Z",
    "title_canon_sha256": "96063a7d179df3bf8b9e04f8aa01b2c30ee7bc1b1c65cfc38a8b46594f4d7290"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.04755",
    "kind": "arxiv",
    "version": 2
  }
}