Pith Number

pith:X56XGVIQ

pith:2015:X56XGVIQNPU3R5HN6DNXY5JA32

not attested not anchored not stored refs pending

Regularity theory for $2$-dimensional almost minimal currents III: blowup

Camillo De Lellis, Emanuele Spadaro, Luca Spolaor

arxiv:1508.05510 v1 · 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{X56XGVIQNPU3R5HN6DNXY5JA32}

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	2026-05-18T01:34:52.328440Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf7d7355106be9b8f4edf0db7c7520de8f1fbdc3cf0733b14ef132cfc506f5be

Aliases

arxiv: 1508.05510 · arxiv_version: 1508.05510v1 · doi: 10.48550/arxiv.1508.05510 · pith_short_12: X56XGVIQNPU3 · pith_short_16: X56XGVIQNPU3R5HN · pith_short_8: X56XGVIQ

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/X56XGVIQNPU3R5HN6DNXY5JA32 \
  | 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: bf7d7355106be9b8f4edf0db7c7520de8f1fbdc3cf0733b14ef132cfc506f5be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21cee21dd823de1aadccc67a4940a36893eaafcef11a10095172d145da075d6d",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-08-22T13:22:05Z",
    "title_canon_sha256": "df7fd7b2b8188e08a1a1d51c4c61d2135544dbc105d359f014a4eeed1c80e186"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.05510",
    "kind": "arxiv",
    "version": 1
  }
}