{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ACWAXO5AT5RAQPX7VPT6NP3Q2N","short_pith_number":"pith:ACWAXO5A","canonical_record":{"source":{"id":"2607.15703","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2026-07-17T07:29:38Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"58a9afcdcb27838e65bff09496c75f0e0cd1eebfc4bf6868cee414e533fbe8c4","abstract_canon_sha256":"91212135d31bd9cb0e28ebae827bf6fb9668e2dfe5056bcae8378ab41955ce92"},"schema_version":"1.0"},"canonical_sha256":"00ac0bbba09f62083effabe7e6bf70d34ed636ba9fa928b99f0619bd104ad812","source":{"kind":"arxiv","id":"2607.15703","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.15703","created_at":"2026-07-20T01:19:05Z"},{"alias_kind":"arxiv_version","alias_value":"2607.15703v1","created_at":"2026-07-20T01:19:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.15703","created_at":"2026-07-20T01:19:05Z"},{"alias_kind":"pith_short_12","alias_value":"ACWAXO5AT5RA","created_at":"2026-07-20T01:19:05Z"},{"alias_kind":"pith_short_16","alias_value":"ACWAXO5AT5RAQPX7","created_at":"2026-07-20T01:19:05Z"},{"alias_kind":"pith_short_8","alias_value":"ACWAXO5A","created_at":"2026-07-20T01:19:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ACWAXO5AT5RAQPX7VPT6NP3Q2N","target":"record","payload":{"canonical_record":{"source":{"id":"2607.15703","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2026-07-17T07:29:38Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"58a9afcdcb27838e65bff09496c75f0e0cd1eebfc4bf6868cee414e533fbe8c4","abstract_canon_sha256":"91212135d31bd9cb0e28ebae827bf6fb9668e2dfe5056bcae8378ab41955ce92"},"schema_version":"1.0"},"canonical_sha256":"00ac0bbba09f62083effabe7e6bf70d34ed636ba9fa928b99f0619bd104ad812","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-20T01:19:05.158333Z","signature_b64":"X5+Asze9NuOVn3ncfpBz+w0rO6QI328nV0Epjzmp/RHkaGZQzYTy3XiXly5bhXUtLioe36UuaORas47PYlMnDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00ac0bbba09f62083effabe7e6bf70d34ed636ba9fa928b99f0619bd104ad812","last_reissued_at":"2026-07-20T01:19:05.157461Z","signature_status":"signed_v1","first_computed_at":"2026-07-20T01:19:05.157461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.15703","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-20T01:19:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mIuNkiyrUh4F0It+z27bQZ1/YjCZOVwSOQBMMv4uKfM4OzYUF/ZPqrAUppXQTX3FIuRYkxoHstkvFwwAh+kCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T21:18:25.088014Z"},"content_sha256":"8ce7eb3f3a9b9b625d50ea567720fd8d2e10bca6b8a16af21aecefd02fb0f910","schema_version":"1.0","event_id":"sha256:8ce7eb3f3a9b9b625d50ea567720fd8d2e10bca6b8a16af21aecefd02fb0f910"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ACWAXO5AT5RAQPX7VPT6NP3Q2N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How Topology Shapes the Phase Behavior of Polyelectrolytes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.soft","authors_text":"Christian Holm, David Beyer, Lena Tarrach, Pierre J. Walker, Zhen-Gang Wang","submitted_at":"2026-07-17T07:29:38Z","abstract_excerpt":"We develop a topology-specific theory of polyelectrolyte coacervation using the random phase approximation and apply it to both simple and complex coacervation. Our results for stars and dendrimers show that more compact chain topologies display a greater propensity for liquid-liquid phase separation, as a function of both Bjerrum length and salt concentration. For mixtures of different topologies, we demonstrate that differences in polymer topology alone are sufficient to drive multiphase coacervation of polyelectrolytes, which we rationalize in terms of an effective $\\chi$ parameter. Analysi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.15703","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.15703/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-20T01:19:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZQTlAZggVVPUw6pPyi3goS6rLY1bkcGec7MkdfByE2EgRuYaz+gWWYCIugxxmspXJybEiun/4aPwWg9TBssfBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T21:18:25.088544Z"},"content_sha256":"664d10c2f4f960045d46677edd83b15b221193664c7fb9df5c07293ebf7390d1","schema_version":"1.0","event_id":"sha256:664d10c2f4f960045d46677edd83b15b221193664c7fb9df5c07293ebf7390d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ACWAXO5AT5RAQPX7VPT6NP3Q2N/bundle.json","state_url":"https://pith.science/pith/ACWAXO5AT5RAQPX7VPT6NP3Q2N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ACWAXO5AT5RAQPX7VPT6NP3Q2N/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-23T21:18:25Z","links":{"resolver":"https://pith.science/pith/ACWAXO5AT5RAQPX7VPT6NP3Q2N","bundle":"https://pith.science/pith/ACWAXO5AT5RAQPX7VPT6NP3Q2N/bundle.json","state":"https://pith.science/pith/ACWAXO5AT5RAQPX7VPT6NP3Q2N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ACWAXO5AT5RAQPX7VPT6NP3Q2N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ACWAXO5AT5RAQPX7VPT6NP3Q2N","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"91212135d31bd9cb0e28ebae827bf6fb9668e2dfe5056bcae8378ab41955ce92","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2026-07-17T07:29:38Z","title_canon_sha256":"58a9afcdcb27838e65bff09496c75f0e0cd1eebfc4bf6868cee414e533fbe8c4"},"schema_version":"1.0","source":{"id":"2607.15703","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.15703","created_at":"2026-07-20T01:19:05Z"},{"alias_kind":"arxiv_version","alias_value":"2607.15703v1","created_at":"2026-07-20T01:19:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.15703","created_at":"2026-07-20T01:19:05Z"},{"alias_kind":"pith_short_12","alias_value":"ACWAXO5AT5RA","created_at":"2026-07-20T01:19:05Z"},{"alias_kind":"pith_short_16","alias_value":"ACWAXO5AT5RAQPX7","created_at":"2026-07-20T01:19:05Z"},{"alias_kind":"pith_short_8","alias_value":"ACWAXO5A","created_at":"2026-07-20T01:19:05Z"}],"graph_snapshots":[{"event_id":"sha256:664d10c2f4f960045d46677edd83b15b221193664c7fb9df5c07293ebf7390d1","target":"graph","created_at":"2026-07-20T01:19:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.15703/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a topology-specific theory of polyelectrolyte coacervation using the random phase approximation and apply it to both simple and complex coacervation. Our results for stars and dendrimers show that more compact chain topologies display a greater propensity for liquid-liquid phase separation, as a function of both Bjerrum length and salt concentration. For mixtures of different topologies, we demonstrate that differences in polymer topology alone are sufficient to drive multiphase coacervation of polyelectrolytes, which we rationalize in terms of an effective $\\chi$ parameter. Analysi","authors_text":"Christian Holm, David Beyer, Lena Tarrach, Pierre J. Walker, Zhen-Gang Wang","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2026-07-17T07:29:38Z","title":"How Topology Shapes the Phase Behavior of Polyelectrolytes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.15703","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8ce7eb3f3a9b9b625d50ea567720fd8d2e10bca6b8a16af21aecefd02fb0f910","target":"record","created_at":"2026-07-20T01:19:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"91212135d31bd9cb0e28ebae827bf6fb9668e2dfe5056bcae8378ab41955ce92","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2026-07-17T07:29:38Z","title_canon_sha256":"58a9afcdcb27838e65bff09496c75f0e0cd1eebfc4bf6868cee414e533fbe8c4"},"schema_version":"1.0","source":{"id":"2607.15703","kind":"arxiv","version":1}},"canonical_sha256":"00ac0bbba09f62083effabe7e6bf70d34ed636ba9fa928b99f0619bd104ad812","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00ac0bbba09f62083effabe7e6bf70d34ed636ba9fa928b99f0619bd104ad812","first_computed_at":"2026-07-20T01:19:05.157461Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-20T01:19:05.157461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X5+Asze9NuOVn3ncfpBz+w0rO6QI328nV0Epjzmp/RHkaGZQzYTy3XiXly5bhXUtLioe36UuaORas47PYlMnDQ==","signature_status":"signed_v1","signed_at":"2026-07-20T01:19:05.158333Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.15703","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ce7eb3f3a9b9b625d50ea567720fd8d2e10bca6b8a16af21aecefd02fb0f910","sha256:664d10c2f4f960045d46677edd83b15b221193664c7fb9df5c07293ebf7390d1"],"state_sha256":"68fe03c5b34bbb88e7c71d78b9076bacee21ebbb7c8aff4d77eb94c3173ecd40"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HG5/4KCqweEdKRuzrW55970Iy0Fh4lcOQSiavQ+70kNGIBK4WBrhID8oi3VGU2b4/1jtDeOByK+FM1jtF3NQBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T21:18:25.093530Z","bundle_sha256":"141b6b8eef06c6500cc13ad7b0dbd82c8c409b62242cbe9c65663d8dde5c3aeb"}}