Pith Number

pith:TXKFVAQH

pith:2025:TXKFVAQHECUJSEJR3I4YKKIPUB

not attested not anchored not stored refs pending

On the extremal functions of second order uncertainty principles: symmetry and symmetry breaking

Chun-Lei Tang, Xiao-ping Chen

arxiv:2508.15221 v1 · 2025-08-21 · 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{TXKFVAQHECUJSEJR3I4YKKIPUB}

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	2026-07-05T11:57:08.467347Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9dd45a820720a8991131da3985290fa0705caccb3fd939c579d5e48a9dbc688c

Aliases

arxiv: 2508.15221 · arxiv_version: 2508.15221v1 · doi: 10.48550/arxiv.2508.15221 · pith_short_12: TXKFVAQHECUJ · pith_short_16: TXKFVAQHECUJSEJR · pith_short_8: TXKFVAQH

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/TXKFVAQHECUJSEJR3I4YKKIPUB \
  | 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: 9dd45a820720a8991131da3985290fa0705caccb3fd939c579d5e48a9dbc688c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a16f88c23883f2136c78e3c0f3afe3e02f384dd26147d5d6a17c4435771fe20c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-08-21T04:19:45Z",
    "title_canon_sha256": "f629b25a209e60148d01170d220160835853b6a247624d905f3bbec4ec1f9cc0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.15221",
    "kind": "arxiv",
    "version": 1
  }
}