Pith Number

pith:4XQFLTXX

pith:2011:4XQFLTXXMR65TJYHWXXB7JNGZK

not attested not anchored not stored refs pending

Lower semicontinuity via W^{1,q}-quasiconvexity

Jean-Philippe Mandallena

arxiv:1106.2828 v7 · 2011-06-14 · math.CA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4XQFLTXXMR65TJYHWXXB7JNGZK}

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	2026-05-18T03:37:53.339949Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5e055cef7647dd9a707b5ee1fa5a6ca894ca8a8796ca8ebcfc7f4e14176cd3c

Aliases

arxiv: 1106.2828 · arxiv_version: 1106.2828v7 · doi: 10.48550/arxiv.1106.2828 · pith_short_12: 4XQFLTXXMR65 · pith_short_16: 4XQFLTXXMR65TJYH · pith_short_8: 4XQFLTXX

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/4XQFLTXXMR65TJYHWXXB7JNGZK \
  | 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: e5e055cef7647dd9a707b5ee1fa5a6ca894ca8a8796ca8ebcfc7f4e14176cd3c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "276dc3d3d4b5f49d77fcfa817fa3a4a1f29411747700b6f2416f2cd80db21825",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-06-14T21:31:03Z",
    "title_canon_sha256": "f01248b5c76ed6a149d5d5f678b971f2aff7470140d749f85df7640ab3fde1b2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.2828",
    "kind": "arxiv",
    "version": 7
  }
}