Field · AI4 / saved conversation 06

Warp a background passage

The original exchange, including tool results and plot images. Expand tool activity to inspect the steps; open a plot to see it full size.

You

In the background-only passage from 1100 to 1250 seconds, slow the first half and catch up in the second half without moving either neighbouring event. Use a strictly monotonic time warp pinned at both endpoints with derivative 1 there; keep all other times and the current event instances unchanged. Treat the endpoints as my selected interval. State the map and show why its derivative stays positive. Use a modest reversible strength, inspect a resolved before/after detail, and verify the whole preserved domain with CompareFunctionStudy. Do not warp event metadata or move the held plateaus.

Tool activity · 37 steps

Starting AI conversation
Preparing context and tools.
Planning tool use
Next tool: InspectFunctionStudy
Using InspectFunctionStudy
```
{
  "revision": ""
}
```
InspectFunctionStudy finished
r7-ebc54198e3ae parent, description, durationSeconds, channels, events, choices, source, liveSourceHash, dirty, selectedIds, selectionSeconds, history, semantics images=0
Planning tool use
Next tool: SelectFunctionStudy

Using SelectFunctionStudy

{
  "endSeconds": 1250,
  "eventIds": [],
  "startSeconds": 1100
}

SelectFunctionStudy finished
r7-ebc54198e3ae parent, description, durationSeconds, channels, events, choices, source, liveSourceHash, dirty, selectedIds, selectionSeconds, history, semantics images=0
Planning tool use
Next tool: ObserveFunctionStudy

Using ObserveFunctionStudy

{
  "compareTo": "",
  "endSeconds": 1150,
  "revision": "r7-ebc54198e3ae",
  "startSeconds": 1125
}

ObserveFunctionStudy finished
r7-ebc54198e3ae intervalSeconds, comparedTo, sourceHash, channels, events, choices, selectedIds, sampling, extrema, holdChecks, joins, difference, imageFile, guarantees, localPeaks images=1
Planning tool use
Next tool: EditFunctionStudy
Using EditFunctionStudy
{"description":"Warp only background passage 1100..1250 with a 6-second C2 delay bump: slow first half, catch up second, positive clock rate and pinned endpoints; preserve all events and other times.","expectedRevision":"r7-ebc54198e3ae","expectedSourceHash":"ebc54198e3aea15a0ca6ce900be84524d3d9ea946a54fd81939f042ac0616f42","source":"import afield.math.functions.Functions\nimport afield.math.functions.StudyComposition\nimport afield.math.functions.StudyEvent\nimport afield.math.functions.StudyChoice\nimport kotlin.math.PI\n\nwith(Functions) {\n val durationSeconds = 3600.0\n val carrierPeriodSeconds = 40.0\n val relativePhasePeriodSeconds = 100.0\n val phaseExcursionRadians = 2.0 * PI / 3.0\n val backgroundC...
EditFunctionStudy finished
r8-e4aea058bc8b Compiled, checked and activated images=0
Planning tool use
Next tool: CompileKotlinRequest

Using CompileKotlinRequest

{
  "file": "afield://function_conversation/function_source/code",
  "runSetupBlocks": false,
  "source": ""
}

CompileKotlinRequest finished
success=true diagnostics=0 setupChanges=0
Planning tool use
Next tool: CompareFunctionStudy

Using CompareFunctionStudy

{
  "afterRevision": "r8-e4aea058bc8b",
  "allowedChannels": [
    "x",
    "y",
    "z"
  ],
  "beforeRevision": "r7-ebc54198e3ae",
  "changedEndSeconds": 1250,
  "changedStartSeconds": 1100
}

CompareFunctionStudy finished
r8-e4aea058bc8b before, allowedIntervalSeconds, allowedChannels, preservedScope, changedEventIds, method images=0
Planning tool use
Next tool: ObserveFunctionStudy

Using ObserveFunctionStudy

{
  "compareTo": "r7-ebc54198e3ae",
  "endSeconds": 1150,
  "revision": "r8-e4aea058bc8b",
  "startSeconds": 1125
}

ObserveFunctionStudy finished
r8-e4aea058bc8b intervalSeconds, comparedTo, sourceHash, channels, events, choices, selectedIds, sampling, extrema, holdChecks, joins, difference, imageFile, guarantees, localPeaks images=1
Planning tool use
Next tool: ObserveFunctionStudy

Using ObserveFunctionStudy

{
  "compareTo": "r7-ebc54198e3ae",
  "endSeconds": 1260,
  "revision": "r8-e4aea058bc8b",
  "startSeconds": 1235
}

ObserveFunctionStudy finished
r8-e4aea058bc8b intervalSeconds, comparedTo, sourceHash, channels, events, choices, selectedIds, sampling, extrema, holdChecks, joins, difference, imageFile, guarantees, localPeaks images=1
Calculating derivatives and endpoints
Calculating derivatives and endpoints

I need to get the correct derivative! I had an earlier maximum at u .276. The derivative of ( u^2 v^2(1-2u) ) simplifies to ( 2uv(1-2u)^2 - 2u^2v^2 ). This leads to a final proof and a coarse bound of .52, which should be enough for the exact values. I also want to sample endpoints and examine the differences with earlier results. I’ll append those to my saved notes for reference.

Next tool: SampleFunctionStudy

Using SampleFunctionStudy

{
  "revision": "r7-ebc54198e3ae",
  "timesSeconds": [
    1100,
    1250
  ]
}

SampleFunctionStudy finished
r7-ebc54198e3ae timesSeconds, channelNames, values, method images=0
Planning tool use
Next tool: SampleFunctionStudy

Using SampleFunctionStudy

{
  "revision": "r8-e4aea058bc8b",
  "timesSeconds": [
    1100,
    1250
  ]
}

SampleFunctionStudy finished
r8-e4aea058bc8b timesSeconds, channelNames, values, method images=0
Planning tool use
Next tool: DocumentGuideReadRequest

Using DocumentGuideReadRequest

{
  "lineCount": 100,
  "path": "guides/working.md",
  "startLine": 99
}

DocumentGuideReadRequest finished
Read guides/working.md lines 99–106
Planning tool use
Next tool: DocumentGuideAppendRequest
Using DocumentGuideAppendRequest
{"path":"guides/working.md","revision":"928435b69837055f6b2f994d58cada7adbc7ebd648de9b0f5c6022ae4d28db16","text":"\n## Background passage warp (activated after e4 deletion)\n\n- r7-ebc54198e3ae removed only e4 (1985..2215 s), retaining r6 in history. Compare r6 -> r7: all channels outside that support have maxAbs/RMS 0 across 168500 samples each. Current event IDs remain e1/e2/e3/e5/e6.\n- New working revision r8-e4aea058bc8b, parent r7. Selected interval is 1100..1250 s with no event IDs. It lies between e2 end 1015 and e3 start 1425.\n- All background components/channels use T(t)=t-A64u^3*(1-u)^3, u=(t-1100)/150, A=6 seconds, only inside that interval; identity elsewhere. Peak delay ...
DocumentGuideAppendRequest finished
Saved guides/working.md

r7-ebc54198e3ae; 1125.0..1150.0 seconds. White=current; dashed grey=none. Inspect local waveforms before judging pulse rate; wide views are min/max envelopes.

r8-e4aea058bc8b; 1125.0..1150.0 seconds. White=current; dashed grey=r7-ebc54198e3ae. Inspect local waveforms before judging pulse rate; wide views are min/max envelopes.

r8-e4aea058bc8b; 1235.0..1260.0 seconds. White=current; dashed grey=r7-ebc54198e3ae. Inspect local waveforms before judging pulse rate; wide views are min/max envelopes.

AI4

Activated r8-e4aea058bc8b, with 1100–1250 s selected.

Time map

All three background channels now use [ T(t)=t-6\cdot64u^3(1-u)^3,\qquad u=\frac{t-1100}{150} ] inside the interval, and (T(t)=t) everywhere else.

This gives a 6-second maximum delay at 1175 s, slowing the first half and catching up in the second. Both endpoints are fixed, with (T'=1) and (T''=0).

Its derivative is [ T'(t)=1-\frac6{150}\,192u^2(1-u)^2(1-2u). ] Since the absolute polynomial factor is bounded by (192/(25\sqrt5)), (0.8626\le T'\le1.1374): time always advances. The map is invertible; setting backgroundWarpPeakDelaySeconds to zero restores the original clock.

Verified

Inspected resolved before/after waveforms at 1125–1150 s, plus recovery at 1235–1260 s.
Exact endpoint values match the previous revision.
CompareFunctionStudy: zero maximum and RMS error outside the selected interval, over 172,500 samples per channel, with no changed event metadata.
All event instances, held plateaus, and e3’s timing and y lag remain unchanged.
Kotlin compilation passed.

Saved the map and evidence in working notes.