Pith Number

pith:4ANYE25J

pith:2026:4ANYE25JFJGEFCVHOHQVZGYAYL

not attested not anchored not stored refs pending

The self-organized vacancy order in Pr$_9$Ge$_{16}$

Aleksandr V. Chernatyskiy, Brianna R. Billingsley, Feng Ye, Gregory T. McCandless, Halyna Hodovanets, Hyunsoo Kim, Jayashani S. T. Wickramasinghe, Julia Y. Chan, Kelci Graville, Liang Wu, Melissa G. Anderson, Simon G. Mitchell, Tai Kong, Zachary J. Morgan

arxiv:2607.12781 v1 · 2026-07-14 · cond-mat.mtrl-sci · cond-mat.str-el

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4ANYE25JFJGEFCVHOHQVZGYAYL}

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	2026-07-15T01:22:17.512251Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e01b826ba92a4c428aa771e15c9b00c2e563563d67024378e84e614e99563ef7

Aliases

arxiv: 2607.12781 · arxiv_version: 2607.12781v1 · doi: 10.48550/arxiv.2607.12781 · pith_short_12: 4ANYE25JFJGE · pith_short_16: 4ANYE25JFJGEFCVH · pith_short_8: 4ANYE25J

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/4ANYE25JFJGEFCVHOHQVZGYAYL \
  | 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: e01b826ba92a4c428aa771e15c9b00c2e563563d67024378e84e614e99563ef7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c9d05e68adf5157baf8fb2978814e06899bb39fa98ab65a7cd193f2f7566a26",
    "cross_cats_sorted": [
      "cond-mat.str-el"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.mtrl-sci",
    "submitted_at": "2026-07-14T13:58:07Z",
    "title_canon_sha256": "060cf6a7ba22e6ad084f6242caffcac733664e8491eda7004373b4be99af7679"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.12781",
    "kind": "arxiv",
    "version": 1
  }
}