Pith Number

pith:VZ5NBGCA

pith:2013:VZ5NBGCANFBDOONXMW2ZRKTTG3

not attested not anchored not stored refs pending

Low energy resolvent for the Hodge Laplacian: Applications to Riesz transform, Sobolev estimates and analytic torsion

Colin Guillarmou, David A. Sher

arxiv:1310.4694 v1 · 2013-10-17 · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VZ5NBGCANFBDOONXMW2ZRKTTG3}

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	2026-05-18T03:10:13.189511Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae7ad0984069423739b765b598aa7336e453a57ce7c1c273d0330e7b7aa525a7

Aliases

arxiv: 1310.4694 · arxiv_version: 1310.4694v1 · doi: 10.48550/arxiv.1310.4694 · pith_short_12: VZ5NBGCANFBD · pith_short_16: VZ5NBGCANFBDOONX · pith_short_8: VZ5NBGCA

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/VZ5NBGCANFBDOONXMW2ZRKTTG3 \
  | 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: ae7ad0984069423739b765b598aa7336e453a57ce7c1c273d0330e7b7aa525a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a119a626363f79c5e2a291cdc457d622286207449094775a7a02aec6600ecc90",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-10-17T13:12:26Z",
    "title_canon_sha256": "d99d6e92e7618b8368807828c2e45d6fcf3bc1c17abb72aa1275a611c69f7d2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.4694",
    "kind": "arxiv",
    "version": 1
  }
}