[FEATURE] Persistent project context, account-synced history, and robust memory management

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

Summary

As a Claude Pro subscriber using Claude Code for a multi-session development project,
I've run into three related UX gaps that significantly hurt the experience compared to
what Claude.ai offers. These feel like foundational issues worth addressing together.

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## Issue 1: Memory is tied to folder path — brittle and breaks silently

Claude Code stores project memory at a path derived from the working directory
(e.g. ~/.claude/projects/C--username-Claude-Projects-MyApp/memory/MEMORY.md).

Problem: If the user renames or moves their project folder, the memory mapping
breaks silently. Claude starts a new session with no context, and the user has no
indication why. There is no warning, no recovery prompt, and no easy way to discover
this has happened.

Expected behavior: Memory should be associated with a named project (user-defined),
not a file system path. Renaming or moving a folder should not destroy session context.

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## Issue 2: No conversation history persistence across sessions

When a Claude Code session ends (terminal closed), the entire conversation history
is lost. The only continuity mechanism is the MEMORY.md file, which requires Claude
to manually write structured notes during the session.

Problem: This places the burden of context preservation entirely on the AI, which
is error-prone and incomplete. Important conversational context, decisions, and
reasoning are lost between sessions.

Expected behavior: Claude Code should persist conversation history per project,
similar to how Claude.ai persists chat history, so users can resume sessions with
full context without relying solely on a manually maintained memory file.

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## Issue 3: Claude Code and Claude.ai are siloed despite same account

Claude Pro subscribers have access to both Claude.ai and Claude Code under the same
account, but the two products share nothing — no conversation history, no project
context, no continuity.

Problem: A user working on a project in Claude Code cannot reference that work
in Claude.ai and vice versa. This is especially confusing when both are logged in
with the same account. Users reasonably expect account-level continuity across
Anthropic products.

Expected behavior: At minimum, Claude Code projects should be visible and
accessible from the Claude.ai interface (similar to ChatGPT Projects), giving users
a unified view of their work across both surfaces.

Proposed Solution

Suggested Solution

Introduce a named Projects system in Claude Code that:

• Identifies projects by a user-defined name, not a file system path
• Persists conversation history per project across sessions
• Syncs project context to the user's Anthropic account
• Makes projects accessible from Claude.ai under the same account

This would bring Claude Code's session continuity up to par with Claude.ai and
dramatically improve the experience for users working on long-running projects.

Alternative Solutions

Chatgpt has the persistent memory in "Projects"

Priority

High - Significant impact on productivity

Feature Category

Other

Use Case Example

• Claude Pro subscriber
• Using Claude Code on Windows 10
• Building a multi-session Android app project spanning weeks
• Discovered these limitations organically during active use

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Additional Context

_No response_