Pith Number

pith:RRP7UIDD

pith:2015:RRP7UIDDRSYVZOI6S5FQ6W4TGG

not attested not anchored not stored refs pending

Regularity and the Behavior of Eigenvalues for Minimizers of a Constrained $Q$-tensor Energy for Liquid Crystals

Daniel Phillips, Patricia Bauman

arxiv:1511.01039 v1 · 2015-11-03 · 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{RRP7UIDDRSYVZOI6S5FQ6W4TGG}

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	2026-05-18T01:27:55.390980Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8c5ffa20638cb15cb91e974b0f5b93319f885a30e178e5355df73b67961040e7

Aliases

arxiv: 1511.01039 · arxiv_version: 1511.01039v1 · doi: 10.48550/arxiv.1511.01039 · pith_short_12: RRP7UIDDRSYV · pith_short_16: RRP7UIDDRSYVZOI6 · pith_short_8: RRP7UIDD

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/RRP7UIDDRSYVZOI6S5FQ6W4TGG \
  | 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: 8c5ffa20638cb15cb91e974b0f5b93319f885a30e178e5355df73b67961040e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e1eafbc57ea8199f9cf05408b580510c5765e73fdbd6416f640241cfce4998e1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-11-03T19:21:39Z",
    "title_canon_sha256": "7f4e242693a994ef0aa67dbdec9a1fe2b42b9d22be57a48296faec6b7d72c3ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.01039",
    "kind": "arxiv",
    "version": 1
  }
}