Pith Number

pith:VNOD3HAY

pith:1999:VNOD3HAYX4WWFGVVRNM3Y7DEX4

not attested not anchored not stored refs pending

Bloch Theory and Quantization of Magnetic Systems

Michael J. Gruber

arxiv:math-ph/9903048 v2 · 1999-03-30 · math-ph · math.MP · math.SP · 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{VNOD3HAYX4WWFGVVRNM3Y7DEX4}

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.

Cited by

1 paper in Pith

Hilbert Space and Defect Hilbert Spaces Associated with Categorical Symmetries

Receipt and verification

First computed	2026-07-04T15:51:29.115428Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab5c3d9c18bf2d629ab58b59bc7c64bf2abe390d600de90e0f0df82bbad6c4a0

Aliases

arxiv: math-ph/9903048 · arxiv_version: math-ph/9903048v2 · doi: 10.48550/arxiv.math-ph/9903048 · pith_short_12: VNOD3HAYX4WW · pith_short_16: VNOD3HAYX4WWFGVV · pith_short_8: VNOD3HAY

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/VNOD3HAYX4WWFGVVRNM3Y7DEX4 \
  | 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: ab5c3d9c18bf2d629ab58b59bc7c64bf2abe390d600de90e0f0df82bbad6c4a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "560803ed51fab843a557b1292967bb95b8440e7998354d3c6391e1915a8fb499",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP",
      "quant-ph"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "1999-03-30T16:50:39Z",
    "title_canon_sha256": "8f5a1287f3d8cfea96e7abe6df110e4718c131fe4867b43e1c15f35687bb9661"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/9903048",
    "kind": "arxiv",
    "version": 2
  }
}