Pith Number

pith:27IBFHZ5

pith:2014:27IBFHZ5KQXOXSHQ25C22VBCJ6

not attested not anchored not stored refs pending

Square Functions and the $A_\infty$ Property of Elliptic Measures

B. Kirchheim, C. Kenig, J. Pipher, T.Toro

arxiv:1409.7131 v1 · 2014-09-25 · 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{27IBFHZ5KQXOXSHQ25C22VBCJ6}

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	2026-05-18T02:41:59.088132Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7d0129f3d542eebc8f0d745ad54224fb60e7e5fda1c27b0d10228d28b88e895

Aliases

arxiv: 1409.7131 · arxiv_version: 1409.7131v1 · doi: 10.48550/arxiv.1409.7131 · pith_short_12: 27IBFHZ5KQXO · pith_short_16: 27IBFHZ5KQXOXSHQ · pith_short_8: 27IBFHZ5

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/27IBFHZ5KQXOXSHQ25C22VBCJ6 \
  | 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: d7d0129f3d542eebc8f0d745ad54224fb60e7e5fda1c27b0d10228d28b88e895

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd8b244350bb0634a1a427b9c4dbb7cb1b6fd1a4b3ac9aae5393996f5295da59",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-09-25T00:51:55Z",
    "title_canon_sha256": "dc200357a79b4f13d7c3cf505939e928a48ea7ff1439bd629ec41d0f69827dc3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.7131",
    "kind": "arxiv",
    "version": 1
  }
}