Skip to content

Scope rank-two native and decoder obstructions (no new κ) #7098

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
rohanarun wants to merge 1 commit into
base: main
Choose a base branch
from
+8,541 −0
Open

Scope rank-two native and decoder obstructions (no new κ) #7098

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
36 changes: 36 additions & 0 deletions research/rank-two-boundary-and-decoder-limits/FOLLOW-UP.md
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,36 @@
# Later decoder and connected-caller checks

These follow-up results use different source interfaces from the frozen BIT
word. Their receipts are supplemental to the registered replay.

- On [#7089](https://github.com/CrocSwap/integer-mult-bounds/pull/7089) head
`3a007633e5f96dcfba428eec4b4f3e32c5c2bd28`, the fixed schedule cannot produce
the fourth uncoded row from its 39 recorded banks with degree-zero left
operators. The dual reads just two coefficients of degree `D1 D3`. Only five
bank and translated-word pairs can meet the dual support, and their terms
cancel. The target pairs to one. A changed entrance did recover four rows in
the formal model, but used odd powers of Q with unpaid implementation.
Reassigning one query under even-Q controls is insufficient in the fixed
two-output late FULL layout. The quotient prefix has odd rank two, while
the two late axes require two additional independent directions. The
[dual receipt](follow-up/PR7089-UNBOUNDED-SUFFIX-DUAL.json) and
[quotient receipt](follow-up/PR7089-ONE-QUERY-ODD-DIMENSION-VERIFIED.json)
document the distinct scopes.
- On [#7002](https://github.com/CrocSwap/integer-mult-bounds/pull/7002) head
`ed1a0a83dfe5d28db9a971bcfc1403bcdc03a49b`, the connected sign header has
a sharp 39-transvection count on 38 roles for the given sign construction.
If 38 rank-one updates produced −I, their update directions would be a basis.
In that basis, the first updated row keeps diagonal entry +1 and is never
modified again. The pinned 39 updates attain −I. With two such updates per
HOST, the three thin units cannot simply be dropped. See the
[sign-header receipt](follow-up/PR7002-SIGN-HEADER-THIN-MINIMUM.json).
- We constructed noncoordinate idle projectors that commute through the
intervening role-level updates of that caller. All 181 incidences remain,
grouped into 76 jobs per port. The exact normalized controls matched all 38
columns in both sign sectors. The raw complex budget, composed with the
retained F+H1 native invoice, still needs at least 821 rank-one cost
equivalents at κ = .005 before any physical or ordinary overhead. This
compares a constructed normalized schedule and a declared native tariff.
It leaves carried directions, different HOST words and BIT admission open.
See the [projectors](follow-up/PR7002-NONCOORDINATE-IDLE-WORD.json) and
[composed budget](follow-up/PR7002-ACTUAL-IDLE-COMPOSITION-BUDGET.json).
201 changes: 201 additions & 0 deletions research/rank-two-boundary-and-decoder-limits/LICENSE
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,201 @@
Apache License
Version 2.0, January 2004
http://www.apache.org/licenses/

TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION

1. Definitions.

"License" shall mean the terms and conditions for use, reproduction,
and distribution as defined by Sections 1 through 9 of this document.

"Licensor" shall mean the copyright owner or entity authorized by
the copyright owner that is granting the License.

"Legal Entity" shall mean the union of the acting entity and all
other entities that control, are controlled by, or are under common
control with that entity. For the purposes of this definition,
"control" means (i) the power, direct or indirect, to cause the
direction or management of such entity, whether by contract or
otherwise, or (ii) ownership of fifty percent (50%) or more of the
outstanding shares, or (iii) beneficial ownership of such entity.

"You" (or "Your") shall mean an individual or Legal Entity
exercising permissions granted by this License.

"Source" form shall mean the preferred form for making modifications,
including but not limited to software source code, documentation
source, and configuration files.

"Object" form shall mean any form resulting from mechanical
transformation or translation of a Source form, including but
not limited to compiled object code, generated documentation,
and conversions to other media types.

"Work" shall mean the work of authorship, whether in Source or
Object form, made available under the License, as indicated by a
copyright notice that is included in or attached to the work
(an example is provided in the Appendix below).

"Derivative Works" shall mean any work, whether in Source or Object
form, that is based on (or derived from) the Work and for which the
editorial revisions, annotations, elaborations, or other modifications
represent, as a whole, an original work of authorship. For the purposes
of this License, Derivative Works shall not include works that remain
separable from, or merely link (or bind by name) to the interfaces of,
the Work and Derivative Works thereof.

"Contribution" shall mean any work of authorship, including
the original version of the Work and any modifications or additions
to that Work or Derivative Works thereof, that is intentionally
submitted to Licensor for inclusion in the Work by the copyright owner
or by an individual or Legal Entity authorized to submit on behalf of
the copyright owner. For the purposes of this definition, "submitted"
means any form of electronic, verbal, or written communication sent
to the Licensor or its representatives, including but not limited to
communication on electronic mailing lists, source code control systems,
and issue tracking systems that are managed by, or on behalf of, the
Licensor for the purpose of discussing and improving the Work, but
excluding communication that is conspicuously marked or otherwise
designated in writing by the copyright owner as "Not a Contribution."

"Contributor" shall mean Licensor and any individual or Legal Entity
on behalf of whom a Contribution has been received by Licensor and
subsequently incorporated within the Work.

2. Grant of Copyright License. Subject to the terms and conditions of
this License, each Contributor hereby grants to You a perpetual,
worldwide, non-exclusive, no-charge, royalty-free, irrevocable
copyright license to reproduce, prepare Derivative Works of,
publicly display, publicly perform, sublicense, and distribute the
Work and such Derivative Works in Source or Object form.

3. Grant of Patent License. Subject to the terms and conditions of
this License, each Contributor hereby grants to You a perpetual,
worldwide, non-exclusive, no-charge, royalty-free, irrevocable
(except as stated in this section) patent license to make, have made,
use, offer to sell, sell, import, and otherwise transfer the Work,
where such license applies only to those patent claims licensable
by such Contributor that are necessarily infringed by their
Contribution(s) alone or by combination of their Contribution(s)
with the Work to which such Contribution(s) was submitted. If You
institute patent litigation against any entity (including a
cross-claim or counterclaim in a lawsuit) alleging that the Work
or a Contribution incorporated within the Work constitutes direct
or contributory patent infringement, then any patent licenses
granted to You under this License for that Work shall terminate
as of the date such litigation is filed.

4. Redistribution. You may reproduce and distribute copies of the
Work or Derivative Works thereof in any medium, with or without
modifications, and in Source or Object form, provided that You
meet the following conditions:

(a) You must give any other recipients of the Work or
Derivative Works a copy of this License; and

(b) You must cause any modified files to carry prominent notices
stating that You changed the files; and

(c) You must retain, in the Source form of any Derivative Works
that You distribute, all copyright, patent, trademark, and
attribution notices from the Source form of the Work,
excluding those notices that do not pertain to any part of
the Derivative Works; and

(d) If the Work includes a "NOTICE" text file as part of its
distribution, then any Derivative Works that You distribute must
include a readable copy of the attribution notices contained
within such NOTICE file, excluding those notices that do not
pertain to any part of the Derivative Works, in at least one
of the following places: within a NOTICE text file distributed
as part of the Derivative Works; within the Source form or
documentation, if provided along with the Derivative Works; or,
within a display generated by the Derivative Works, if and
wherever such third-party notices normally appear. The contents
of the NOTICE file are for informational purposes only and
do not modify the License. You may add Your own attribution
notices within Derivative Works that You distribute, alongside
or as an addendum to the NOTICE text from the Work, provided
that such additional attribution notices cannot be construed
as modifying the License.

You may add Your own copyright statement to Your modifications and
may provide additional or different license terms and conditions
for use, reproduction, or distribution of Your modifications, or
for any such Derivative Works as a whole, provided Your use,
reproduction, and distribution of the Work otherwise complies with
the conditions stated in this License.

5. Submission of Contributions. Unless You explicitly state otherwise,
any Contribution intentionally submitted for inclusion in the Work
by You to the Licensor shall be under the terms and conditions of
this License, without any additional terms or conditions.
Notwithstanding the above, nothing herein shall supersede or modify
the terms of any separate license agreement you may have executed
with Licensor regarding such Contributions.

6. Trademarks. This License does not grant permission to use the trade
names, trademarks, service marks, or product names of the Licensor,
except as required for reasonable and customary use in describing the
origin of the Work and reproducing the content of the NOTICE file.

7. Disclaimer of Warranty. Unless required by applicable law or
agreed to in writing, Licensor provides the Work (and each
Contributor provides its Contributions) on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
implied, including, without limitation, any warranties or conditions
of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
PARTICULAR PURPOSE. You are solely responsible for determining the
appropriateness of using or redistributing the Work and assume any
risks associated with Your exercise of permissions under this License.

8. Limitation of Liability. In no event and under no legal theory,
whether in tort (including negligence), contract, or otherwise,
unless required by applicable law (such as deliberate and grossly
negligent acts) or agreed to in writing, shall any Contributor be
liable to You for damages, including any direct, indirect, special,
incidental, or consequential damages of any character arising as a
result of this License or out of the use or inability to use the
Work (including but not limited to damages for loss of goodwill,
work stoppage, computer failure or malfunction, or any and all
other commercial damages or losses), even if such Contributor
has been advised of the possibility of such damages.

9. Accepting Warranty or Additional Liability. While redistributing
the Work or Derivative Works thereof, You may choose to offer,
and charge a fee for, acceptance of support, warranty, indemnity,
or other liability obligations and/or rights consistent with this
License. However, in accepting such obligations, You may act only
on Your own behalf and on Your sole responsibility, not on behalf
of any other Contributor, and only if You agree to indemnify,
defend, and hold each Contributor harmless for any liability
incurred by, or claims asserted against, such Contributor by reason
of your accepting any such warranty or additional liability.

END OF TERMS AND CONDITIONS

APPENDIX: How to apply the Apache License to your work.

To apply the Apache License to your work, attach the following
boilerplate notice, with the fields enclosed by brackets "[]"
replaced with your own identifying information. (Don't include
the brackets!) The text should be enclosed in the appropriate
comment syntax for the file format. We also recommend that a
file or class name and description of purpose be included on the
same "printed page" as the copyright notice for easier
identification within third-party archives.

Copyright [yyyy] [name of copyright owner]

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
80 changes: 80 additions & 0 deletions research/rank-two-boundary-and-decoder-limits/README.md
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,80 @@
# Rank-two native and decoder limits on the path to κ = .01

We tested whether a second protected direction could improve the signed recursive
invoice of a fixed BIT native word. The frozen-boundary obstruction, the two
propagation screens and the 45-port caller cost check all held up in the
replay included here. The experiments also give an exact local source worth
retaining for a redesigned caller.

## What the checks establish

- **Frozen neighbors.** On the 27,818-event six-helper-handoff word, exact
rational nullspaces give zero initial extension and zero terminal shrink
dimension on all 111 ports. The calculation takes the same-chart ADD
components between MOVE and CLEAR events into account. It holds with the
adjacent frame subspaces fixed.
- **Propagating the frame changes.** The saved profiles contain 6,993
single-seed cases and 8,040 selected paired or collective cases. Every
profile worsens the native helper-minus-paid moment at κ = .005, .006
and .01, with no independent main-output credit. At .01 the best deltas
are about −51.4191 and −36.0921 respectively. The paired census used up
to twelve leading seeds per direction for pair tests and one simultaneous
seed set. The published replay rechecks every saved price with integer
interval arithmetic. It does not regenerate the propagation census.
- **A source that passes locally.** Fused boundary bridges protected 45
planes simultaneously. The retained normalized source receipt covers
775 arbitrary input and scratch columns. The separate audit covers the
rational frames, ownership and nested-query identities. Paid rank mass
stays 5,129, with a small increase in the concave moment. Physical BIT
phases, address semantics and arbitrary tensor width are still open.
- **Its existing caller tariff fails.** The old four-factor main path has
off-diagonal rank at most `2+6+6+6=20`. For block matrices,
`B(MN)=A(M)B(N)+B(M)D(N)`, so the bound follows by rank subadditivity.
The declared target tariff grants the other main outputs, pure centers and
helpers and charges no decoder. It still has signed margin below
−154.532 at κ = .005 and below −283.109 at κ = .01. This applies to the
declared target tariff and that factored path. A different allocation or
caller remains open.

There is no new conditional κ claim here. In particular the historical
rank-two and free-shear screens were conditional budgets for unbuilt
constructions. The five inherited framework assumptions and the matching
complex/BIT, physical, precision and outer obligations remain.

## Reproduce

From this directory, run `python3 -B verify.py` using Python 3.10 or newer.
The checker verifies the public evidence hashes, regenerates the exact
111-port nullspaces from the normalized word and frame data, reprices all
15,033 saved profiles at the three specified thresholds, and recomputes
the 45-port tariff signs. It works without a network or solver. Historical
checks on the emitted 45-port word are preserved as receipts. The standalone
replay here covers its tariff and does not rerun that full word.

[Evidence provenance](evidence/provenance.json) records original source
hashes, the exact retained frames and word, and the projection used to
package the saved price inputs. [Follow-up](FOLLOW-UP.md) records the later
connected-caller and decoder checks separately.

## Open next questions

1. Can a revised native path keep rank-seven diagonals while protecting a
second direction? Start by changing one ADD component and checking all
affected helper endpoints and the actual paid profile.
2. Can a different productive caller use the protected planes without the
rank-20 factored path? Start with exact forward and reverse endpoint
checks and price the whole proposed target bank before adding a decoder.
3. Can one paid transport carry the required repair over multiple cuts
without increasing its rank or changing another output? Keep all
arbitrary owners, and charge finite phase, scalar and cleanup work.

## Credit

Rohan Arun, with substantial OpenAI Codex assistance and Claude-assisted
earlier route exploration. The retained native and frame lineage includes
DreamingOfClouds' [#589](https://github.com/CrocSwap/integer-mult-bounds/pull/589)
and its retained predecessors. The later comparisons use unpaidmoon's
[#7089](https://github.com/CrocSwap/integer-mult-bounds/pull/7089) and CubeJerry's
[#6824](https://github.com/CrocSwap/integer-mult-bounds/pull/6824) and
[#7002](https://github.com/CrocSwap/integer-mult-bounds/pull/7002).
New material is Apache-2.0.
18 changes: 18 additions & 0 deletions research/rank-two-boundary-and-decoder-limits/SOURCES.json
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,18 @@
{
"schema_version": 1,
"base_commit": "17469fff78c22941280f04d39dc5a1faee09c840",
"files": [
{
"path": "docs/research/agent-task-catalog.json",
"usage": "provenance",
"git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec",
"sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81"
},
{
"path": "certificates/selected-result.json",
"usage": "provenance",
"git_blob": "d59b5035e7b4cbaa9d688a1d32dd0d6eb79c466a",
"sha256": "9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa"
}
]
}
Loading