Pith Number

pith:UK3I7JBU

pith:2015:UK3I7JBUO7DRNUBHSRJ246UBFK

not attested not anchored not stored refs pending

Regularity theory for $2$-dimensional almost minimal currents II: branched center manifold

Camillo De Lellis, Emanuele Spadaro, Luca Spolaor

arxiv:1508.05509 v2 · 2015-08-22 · 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{UK3I7JBUO7DRNUBHSRJ246UBFK}

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	2026-05-18T00:36:10.079368Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2b68fa43477c716d0279453ae7a812a898f8c30667f0ba5764969a38c804ba0

Aliases

arxiv: 1508.05509 · arxiv_version: 1508.05509v2 · doi: 10.48550/arxiv.1508.05509 · pith_short_12: UK3I7JBUO7DR · pith_short_16: UK3I7JBUO7DRNUBH · pith_short_8: UK3I7JBU

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/UK3I7JBUO7DRNUBHSRJ246UBFK \
  | 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: a2b68fa43477c716d0279453ae7a812a898f8c30667f0ba5764969a38c804ba0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47de604ff5dcf6b4a28f9c2fae90517b47eadf3e6b1d3021943b875649f6d82b",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-08-22T13:15:53Z",
    "title_canon_sha256": "e6fcc187b87ba4f332e7c9c1a5b3e5abb0bfffe0c2ccf69321e829c18408ad6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.05509",
    "kind": "arxiv",
    "version": 2
  }
}