Pith Number

pith:67ULD5LY

pith:2010:67ULD5LYHCOPFL3SN37PKIYYXV

not attested not anchored not stored refs pending

Some new Bellman functions and subordination by orthogonal martingales in $L^{p}, 1<p\le 2$

Alexander Volberg, Prabhu Janakiraman, Vasily Vasyunin

arxiv:1012.0947 v1 · 2010-12-04 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{67ULD5LYHCOPFL3SN37PKIYYXV}

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	2026-05-18T04:34:02.062126Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7e8b1f578389cf2af726efef52318bd69873875c00193ea5f9f2a2fd865da43

Aliases

arxiv: 1012.0947 · arxiv_version: 1012.0947v1 · doi: 10.48550/arxiv.1012.0947 · pith_short_12: 67ULD5LYHCOP · pith_short_16: 67ULD5LYHCOPFL3S · pith_short_8: 67ULD5LY

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/67ULD5LYHCOPFL3SN37PKIYYXV \
  | 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: f7e8b1f578389cf2af726efef52318bd69873875c00193ea5f9f2a2fd865da43

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e44c3d2e94c4695f68ad0ce904ad6cc305eaaedae4a6b7682763e422da97f54",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-12-04T20:31:13Z",
    "title_canon_sha256": "f807716e9aa250c4510935ceb902bcde0c78d91b7b16b4c6a6cee40fcb201f72"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0947",
    "kind": "arxiv",
    "version": 1
  }
}