Pith Number

pith:TPAF45TJ

pith:2014:TPAF45TJJTRKSS4KV4B6OT3JFG

not attested not anchored not stored refs pending

Decomposition of direct product at an arbitrary Brillouin zone point: $D^{(\bigstar{R})(m)}$ $\otimes$ $D^{(\bigstar{-R})(m)}$

Jian Li, Jiufeng J. Tu, Joseph L. Birman

arxiv:1405.0467 v1 · 2014-03-04 · cond-mat.mtrl-sci

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TPAF45TJJTRKSS4KV4B6OT3JFG}

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	2026-05-18T02:52:42.587881Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9bc05e76694ce2a94b8aaf03e74f69299c2dd6adf8e9fde2c36470371e957c8c

Aliases

arxiv: 1405.0467 · arxiv_version: 1405.0467v1 · doi: 10.48550/arxiv.1405.0467 · pith_short_12: TPAF45TJJTRK · pith_short_16: TPAF45TJJTRKSS4K · pith_short_8: TPAF45TJ

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/TPAF45TJJTRKSS4KV4B6OT3JFG \
  | 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: 9bc05e76694ce2a94b8aaf03e74f69299c2dd6adf8e9fde2c36470371e957c8c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "28679cb4cd7af4a5f6d4e3a55e9ebf5ab071158894ef206326e5b9331ceca2a7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.mtrl-sci",
    "submitted_at": "2014-03-04T03:05:25Z",
    "title_canon_sha256": "31d9ea13b1560e2205f3f4019514e1650a7954d30c2e8f757f0e2d94f7fa46d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1405.0467",
    "kind": "arxiv",
    "version": 1
  }
}