Pith Number

pith:UKW5QCQZ

pith:2016:UKW5QCQZWADHEA2RZSTNWJAQEF

not attested not anchored not stored refs pending

Mathematical Theory for Quantum Phase Transitions

Da-peng Li, Jiayan Yang, Ruikuan Liu, Tian Ma

arxiv:1610.06988 v2 · 2016-10-22 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UKW5QCQZWADHEA2RZSTNWJAQEF}

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	2026-05-18T00:55:33.915451Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2add80a19b006720351cca6db241021561d1d33be60b9e7b228e57869c244f0

Aliases

arxiv: 1610.06988 · arxiv_version: 1610.06988v2 · doi: 10.48550/arxiv.1610.06988 · pith_short_12: UKW5QCQZWADH · pith_short_16: UKW5QCQZWADHEA2R · pith_short_8: UKW5QCQZ

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/UKW5QCQZWADHEA2RZSTNWJAQEF \
  | 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: a2add80a19b006720351cca6db241021561d1d33be60b9e7b228e57869c244f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63dc487f9f3a048675e357b9547da79beaf414e4c9fd45fab97f4f9a382cbd32",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-10-22T02:10:30Z",
    "title_canon_sha256": "0593b0b706c313a282f5831723d51f5c83bc861d41576f952718d967b07ac063"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.06988",
    "kind": "arxiv",
    "version": 2
  }
}