Pith Number

pith:DXZLQHK6

pith:2015:DXZLQHK6EZSVKKWTBO3EZS6PFT

not attested not anchored not stored refs pending

Bloch Waves in Crystals and Periodic High Contrast Media

Robert Lipton, Robert Viator Jr

arxiv:1512.06062 v2 · 2015-12-18 · 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{DXZLQHK6EZSVKKWTBO3EZS6PFT}

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	2026-05-18T01:16:24.446425Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1df2b81d5e2665552ad30bb64ccbcf2cc13ad7cef873a835a79cf417b8cf10ab

Aliases

arxiv: 1512.06062 · arxiv_version: 1512.06062v2 · doi: 10.48550/arxiv.1512.06062 · pith_short_12: DXZLQHK6EZSV · pith_short_16: DXZLQHK6EZSVKKWT · pith_short_8: DXZLQHK6

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/DXZLQHK6EZSVKKWTBO3EZS6PFT \
  | 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: 1df2b81d5e2665552ad30bb64ccbcf2cc13ad7cef873a835a79cf417b8cf10ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56fedf7dbbea18bfb42bcf8b9f661423f7cf3496f107cec57c1ce06130c1f522",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-12-18T18:01:39Z",
    "title_canon_sha256": "7893ecc6117d64dba2c4e049feabaf49f1a06782c509b0008779d580db6f38e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06062",
    "kind": "arxiv",
    "version": 2
  }
}