Pith Number

pith:IKGAL2WP

pith:2015:IKGAL2WPCIC3THBEIPAPGUEV73

not attested not anchored not stored refs pending

The Dirac Operator on Regular Metric Trees

Xiao Liu

arxiv:1507.03560 v1 · 2015-07-08 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IKGAL2WPCIC3THBEIPAPGUEV73}

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	2026-05-18T01:36:58.534737Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

428c05eacf1205b99c2443c0f35095fec7dfb12158f30e67c997b87f01dc9791

Aliases

arxiv: 1507.03560 · arxiv_version: 1507.03560v1 · doi: 10.48550/arxiv.1507.03560 · pith_short_12: IKGAL2WPCIC3 · pith_short_16: IKGAL2WPCIC3THBE · pith_short_8: IKGAL2WP

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/IKGAL2WPCIC3THBEIPAPGUEV73 \
  | 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: 428c05eacf1205b99c2443c0f35095fec7dfb12158f30e67c997b87f01dc9791

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4c2ae1969f50d129ab1325fc016c17d8bcb044bb8e6d43adfca0768a4ad7bfe",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-07-08T21:23:15Z",
    "title_canon_sha256": "9b8b0fa500eb201040f559ef8f40c418a621eaa0cc30c8ecee8ce10eef918789"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.03560",
    "kind": "arxiv",
    "version": 1
  }
}