Pith Number

pith:4R6U4E4C

pith:2025:4R6U4E4CNFZWBI33U5YZFDI5LU

not attested not anchored not stored refs pending

The volume of marginally trapped submanifolds in a Lorentzian manifold satisfying the null energy condition

Riku Kishida

arxiv:2506.07093 v1 · 2025-06-08 · 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{4R6U4E4CNFZWBI33U5YZFDI5LU}

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	2026-07-05T11:18:01.165586Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e47d4e1382697360a37ba771928d1d5d3441f2a32de45d80b98413fe19400553

Aliases

arxiv: 2506.07093 · arxiv_version: 2506.07093v1 · doi: 10.48550/arxiv.2506.07093 · pith_short_12: 4R6U4E4CNFZW · pith_short_16: 4R6U4E4CNFZWBI33 · pith_short_8: 4R6U4E4C

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/4R6U4E4CNFZWBI33U5YZFDI5LU \
  | 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: e47d4e1382697360a37ba771928d1d5d3441f2a32de45d80b98413fe19400553

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "471610967ccfcb1015bb7584cb175a52151156a064215592a918a70db26f8661",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-06-08T11:34:54Z",
    "title_canon_sha256": "4b013dbf76a8f3f87d8e82a9fa823a5d2b89e5965cde1e4bb5b136a84926a9a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.07093",
    "kind": "arxiv",
    "version": 1
  }
}