Pith Number

pith:WCEYB6GF

pith:2021:WCEYB6GFKHGZTX6P6UJKT5P4GL

not attested not anchored not stored refs pending

On universally optimal lattice phase transitions and energy minimizers of completely monotone potentials

Juncheng Wei, Senping Luo, Wenming Zou

arxiv:2110.08728 v1 · 2021-10-17 · math.CA · math-ph · math.MP

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WCEYB6GFKHGZTX6P6UJKT5P4GL}

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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

Signs of high order derivatives for the theta and Epstein zeta functions and application

Receipt and verification

First computed	2026-07-05T03:23:19.869301Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b08980f8c551cd99dfcff512a9f5fc32e2b028ffbf2c80c1010afe1cf8aff8b5

Aliases

arxiv: 2110.08728 · arxiv_version: 2110.08728v1 · doi: 10.48550/arxiv.2110.08728 · pith_short_12: WCEYB6GFKHGZ · pith_short_16: WCEYB6GFKHGZTX6P · pith_short_8: WCEYB6GF

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/WCEYB6GFKHGZTX6P6UJKT5P4GL \
  | 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: b08980f8c551cd99dfcff512a9f5fc32e2b028ffbf2c80c1010afe1cf8aff8b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4116934b0fd7c3579c91c86ad419ac5ac75a49dd71382bb75730d07a1c07452e",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2021-10-17T05:39:57Z",
    "title_canon_sha256": "6850b7d4133abb7c56c5e016f917a5e7fca8ef81329cc4f7a2c3a191bae8ac03"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2110.08728",
    "kind": "arxiv",
    "version": 1
  }
}