Pith Number

pith:HSYJ43J5

pith:2021:HSYJ43J5GG52VDLLN2RW5X5LUD

not attested not anchored not stored refs pending

Marginal tubes and foliations by marginal surfaces

Pengyu Le

arxiv:2109.08888 v4 · 2021-09-18 · math.DG · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HSYJ43J5GG52VDLLN2RW5X5LUD}

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	2026-07-05T05:42:22.068655Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3cb09e6d3d31bbaa8d6b6ea36edfaba0f8294f5008fd4c267a8cdb8a33084d7a

Aliases

arxiv: 2109.08888 · arxiv_version: 2109.08888v4 · doi: 10.48550/arxiv.2109.08888 · pith_short_12: HSYJ43J5GG52 · pith_short_16: HSYJ43J5GG52VDLL · pith_short_8: HSYJ43J5

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/HSYJ43J5GG52VDLLN2RW5X5LUD \
  | 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: 3cb09e6d3d31bbaa8d6b6ea36edfaba0f8294f5008fd4c267a8cdb8a33084d7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "70aff190adf2edfd7a7e712a8cf9d35167bb02ad7e2cc2b6d7aba01e027ce565",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2021-09-18T09:15:37Z",
    "title_canon_sha256": "93e473574ee8f2a5fe922660c586ce53da5511bb97a1cc7837d1d7b736c0697c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.08888",
    "kind": "arxiv",
    "version": 4
  }
}