{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:S7STO2SPI2HOKQNHPGTV4HDADK","short_pith_number":"pith:S7STO2SP","canonical_record":{"source":{"id":"cond-mat/0702590","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-02-26T12:45:28Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.soft"],"title_canon_sha256":"eef2d1ca6931d9cf0691fb15a604e53db3c99f2fbb494e713b2501a151a411e5","abstract_canon_sha256":"61792dc6328d8368661e676e28a4dc0b791fb6ade870e8fa75de202799e9cef5"},"schema_version":"1.0"},"canonical_sha256":"97e5376a4f468ee541a779a75e1c601ab289e3a47caaa589137369e80a8761ac","source":{"kind":"arxiv","id":"cond-mat/0702590","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0702590","created_at":"2026-05-18T03:32:32Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0702590v2","created_at":"2026-05-18T03:32:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0702590","created_at":"2026-05-18T03:32:32Z"},{"alias_kind":"pith_short_12","alias_value":"S7STO2SPI2HO","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"S7STO2SPI2HOKQNH","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"S7STO2SP","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:S7STO2SPI2HOKQNHPGTV4HDADK","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0702590","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-02-26T12:45:28Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.soft"],"title_canon_sha256":"eef2d1ca6931d9cf0691fb15a604e53db3c99f2fbb494e713b2501a151a411e5","abstract_canon_sha256":"61792dc6328d8368661e676e28a4dc0b791fb6ade870e8fa75de202799e9cef5"},"schema_version":"1.0"},"canonical_sha256":"97e5376a4f468ee541a779a75e1c601ab289e3a47caaa589137369e80a8761ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:32.301273Z","signature_b64":"Lj1s9XU57vProVABqC0Vk/07M7tiUFWjRUhhmLO1ARqpnJs9FLNg86D6d6lHoWO32OQyoRFwrbWfkIttFxrxCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97e5376a4f468ee541a779a75e1c601ab289e3a47caaa589137369e80a8761ac","last_reissued_at":"2026-05-18T03:32:32.300322Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:32.300322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0702590","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:32:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ino6YkbOinCWpgBicehhaHSAbRymzhC7T1DtfdGoynKcYbeLzAYWMtg1QbWaECXcQTlo0kGQcLNfkr5AGApgAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:11:22.545072Z"},"content_sha256":"74acf36c0e231c269a224c85bf3baaf6f43f86eb9a935ddcd2b2b1c406608344","schema_version":"1.0","event_id":"sha256:74acf36c0e231c269a224c85bf3baaf6f43f86eb9a935ddcd2b2b1c406608344"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:S7STO2SPI2HOKQNHPGTV4HDADK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variational bounds for the shear viscosity of gelling melts","license":"","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.soft"],"primary_cat":"cond-mat.stat-mech","authors_text":"Annette Zippelius, Claas H. K\\\"ohler, Henning L\\\"owe, Peter M\\\"uller","submitted_at":"2007-02-26T12:45:28Z","abstract_excerpt":"We study shear stress relaxation for a gelling melt of randomly crosslinked, interacting monomers. We derive a lower bound for the static shear viscosity $\\eta$, which implies that it diverges algebraically with a critical exponent $k\\ge 2\\nu-\\beta$. Here, $\\nu$ and $\\beta$ are the critical exponents of percolation theory for the correlation length and the gel fraction. In particular, the divergence is stronger than in the Rouse model, proving the relevance of excluded-volume interactions for the dynamic critical behaviour at the gel transition. Precisely at the critical point, our exact resul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0702590","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T03:32:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wBD5SkFs45UfGDnP2oYO69S1ETdIXu4ic2l1eSaM1nshNlgCBrWarzxK4R/WU4lr57fS4w/l5dQz6ObSdOGECQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:11:22.545792Z"},"content_sha256":"e7ad2003583bcd1fa3fb3598af7cd7b76416a77c597742d115b035360e74fca9","schema_version":"1.0","event_id":"sha256:e7ad2003583bcd1fa3fb3598af7cd7b76416a77c597742d115b035360e74fca9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S7STO2SPI2HOKQNHPGTV4HDADK/bundle.json","state_url":"https://pith.science/pith/S7STO2SPI2HOKQNHPGTV4HDADK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S7STO2SPI2HOKQNHPGTV4HDADK/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":"2026-06-06T15:11:22Z","links":{"resolver":"https://pith.science/pith/S7STO2SPI2HOKQNHPGTV4HDADK","bundle":"https://pith.science/pith/S7STO2SPI2HOKQNHPGTV4HDADK/bundle.json","state":"https://pith.science/pith/S7STO2SPI2HOKQNHPGTV4HDADK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S7STO2SPI2HOKQNHPGTV4HDADK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:S7STO2SPI2HOKQNHPGTV4HDADK","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":"61792dc6328d8368661e676e28a4dc0b791fb6ade870e8fa75de202799e9cef5","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.soft"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-02-26T12:45:28Z","title_canon_sha256":"eef2d1ca6931d9cf0691fb15a604e53db3c99f2fbb494e713b2501a151a411e5"},"schema_version":"1.0","source":{"id":"cond-mat/0702590","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0702590","created_at":"2026-05-18T03:32:32Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0702590v2","created_at":"2026-05-18T03:32:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0702590","created_at":"2026-05-18T03:32:32Z"},{"alias_kind":"pith_short_12","alias_value":"S7STO2SPI2HO","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"S7STO2SPI2HOKQNH","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"S7STO2SP","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:e7ad2003583bcd1fa3fb3598af7cd7b76416a77c597742d115b035360e74fca9","target":"graph","created_at":"2026-05-18T03:32:32Z","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"},"paper":{"abstract_excerpt":"We study shear stress relaxation for a gelling melt of randomly crosslinked, interacting monomers. We derive a lower bound for the static shear viscosity $\\eta$, which implies that it diverges algebraically with a critical exponent $k\\ge 2\\nu-\\beta$. Here, $\\nu$ and $\\beta$ are the critical exponents of percolation theory for the correlation length and the gel fraction. In particular, the divergence is stronger than in the Rouse model, proving the relevance of excluded-volume interactions for the dynamic critical behaviour at the gel transition. Precisely at the critical point, our exact resul","authors_text":"Annette Zippelius, Claas H. K\\\"ohler, Henning L\\\"owe, Peter M\\\"uller","cross_cats":["cond-mat.dis-nn","cond-mat.soft"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-02-26T12:45:28Z","title":"Variational bounds for the shear viscosity of gelling melts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0702590","kind":"arxiv","version":2},"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":"sha256:74acf36c0e231c269a224c85bf3baaf6f43f86eb9a935ddcd2b2b1c406608344","target":"record","created_at":"2026-05-18T03:32:32Z","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":"61792dc6328d8368661e676e28a4dc0b791fb6ade870e8fa75de202799e9cef5","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.soft"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2007-02-26T12:45:28Z","title_canon_sha256":"eef2d1ca6931d9cf0691fb15a604e53db3c99f2fbb494e713b2501a151a411e5"},"schema_version":"1.0","source":{"id":"cond-mat/0702590","kind":"arxiv","version":2}},"canonical_sha256":"97e5376a4f468ee541a779a75e1c601ab289e3a47caaa589137369e80a8761ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97e5376a4f468ee541a779a75e1c601ab289e3a47caaa589137369e80a8761ac","first_computed_at":"2026-05-18T03:32:32.300322Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:32.300322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lj1s9XU57vProVABqC0Vk/07M7tiUFWjRUhhmLO1ARqpnJs9FLNg86D6d6lHoWO32OQyoRFwrbWfkIttFxrxCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:32.301273Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0702590","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74acf36c0e231c269a224c85bf3baaf6f43f86eb9a935ddcd2b2b1c406608344","sha256:e7ad2003583bcd1fa3fb3598af7cd7b76416a77c597742d115b035360e74fca9"],"state_sha256":"c7c198456ec01809e5a6757d1085e02f5ff71d5492911bd8189cf99267039e4d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ac89V64P+k0+0G4dWX08vgGbndjh8VrNGXTqHHE1ZTIOBX8p/fcvpHcBaxzPMM5bNtxU4IMBp/LVNUiSg+SYBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T15:11:22.550496Z","bundle_sha256":"893a0b76b82bc4e05e6a9e7b5662e131fc62cfe3270f541614823f40507ab310"}}