{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WWVMNBA3WSHUXPM7XKWJVRMPW6","short_pith_number":"pith:WWVMNBA3","canonical_record":{"source":{"id":"1301.2449","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-11T10:56:46Z","cross_cats_sorted":["math-ph","math.CA","math.MP","math.RT"],"title_canon_sha256":"752272ab987415103001af889c60dbb02d79267235f3c32339ccfb4ef4cfd486","abstract_canon_sha256":"b4131565a72a101859ff8474dfc3ad5f7c8f2085a39bfeb4dfcbab5339c8cc15"},"schema_version":"1.0"},"canonical_sha256":"b5aac6841bb48f4bbd9fbaac9ac58fb792d4ae8b7cf595c35f8a87f8b3f663dc","source":{"kind":"arxiv","id":"1301.2449","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2449","created_at":"2026-05-18T02:32:14Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2449v3","created_at":"2026-05-18T02:32:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2449","created_at":"2026-05-18T02:32:14Z"},{"alias_kind":"pith_short_12","alias_value":"WWVMNBA3WSHU","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WWVMNBA3WSHUXPM7","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WWVMNBA3","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WWVMNBA3WSHUXPM7XKWJVRMPW6","target":"record","payload":{"canonical_record":{"source":{"id":"1301.2449","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-11T10:56:46Z","cross_cats_sorted":["math-ph","math.CA","math.MP","math.RT"],"title_canon_sha256":"752272ab987415103001af889c60dbb02d79267235f3c32339ccfb4ef4cfd486","abstract_canon_sha256":"b4131565a72a101859ff8474dfc3ad5f7c8f2085a39bfeb4dfcbab5339c8cc15"},"schema_version":"1.0"},"canonical_sha256":"b5aac6841bb48f4bbd9fbaac9ac58fb792d4ae8b7cf595c35f8a87f8b3f663dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:14.561503Z","signature_b64":"7Ifm+/6S0U2daLHc9MvGU3Qx9uZIwgGMMV/s0AnOTQHlZq2ptkNXrYwWk3DJgxZHYW44AG9YW6gK2obEDriNDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5aac6841bb48f4bbd9fbaac9ac58fb792d4ae8b7cf595c35f8a87f8b3f663dc","last_reissued_at":"2026-05-18T02:32:14.560843Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:14.560843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.2449","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ch0L2zxQ090/m11wvi2c03ehvr42XMSu1OQKEA2ujig41QokrynWIaSoKOJX7/+cn+hAY1Lkc5DuLvW411yTCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:19:05.368564Z"},"content_sha256":"994d1451b49dc48e1ad30258e241d27c237c0b8b4e6f2b5d84dee02f0e45620f","schema_version":"1.0","event_id":"sha256:994d1451b49dc48e1ad30258e241d27c237c0b8b4e6f2b5d84dee02f0e45620f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WWVMNBA3WSHUXPM7XKWJVRMPW6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complete monotonicity for inverse powers of some combinatorially defined polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP","math.RT"],"primary_cat":"math.CO","authors_text":"Alan D. Sokal, Alexander D. Scott","submitted_at":"2013-01-11T10:56:46Z","abstract_excerpt":"We prove the complete monotonicity on $(0,\\infty)^n$ for suitable inverse powers of the spanning-tree polynomials of graphs and, more generally, of the basis generating polynomials of certain classes of matroids. This generalizes a result of Szego and answers, among other things, a long-standing question of Lewy and Askey concerning the positivity of Taylor coefficients for certain rational functions. Our proofs are based on two_ab initio_ methods for proving that $P^{-\\beta}$ is completely monotone on a convex cone $C$: the determinantal method and the quadratic-form method. These methods are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2449","kind":"arxiv","version":3},"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":"2026-05-18T02:32:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iKKeWnLAUYM/g19QEHd4Swyd0idfIRp5QmBJvDsuIFDRFuAwAf4BZaaqBBgaVq0XLsEHe/YPJdiqVWNN+HtNDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:19:05.369205Z"},"content_sha256":"008068867be74a8b1ec62ef29cd8b21db8cfc365c512cf5ac90f799314a46e3a","schema_version":"1.0","event_id":"sha256:008068867be74a8b1ec62ef29cd8b21db8cfc365c512cf5ac90f799314a46e3a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WWVMNBA3WSHUXPM7XKWJVRMPW6/bundle.json","state_url":"https://pith.science/pith/WWVMNBA3WSHUXPM7XKWJVRMPW6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WWVMNBA3WSHUXPM7XKWJVRMPW6/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":"2026-05-26T15:19:05Z","links":{"resolver":"https://pith.science/pith/WWVMNBA3WSHUXPM7XKWJVRMPW6","bundle":"https://pith.science/pith/WWVMNBA3WSHUXPM7XKWJVRMPW6/bundle.json","state":"https://pith.science/pith/WWVMNBA3WSHUXPM7XKWJVRMPW6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WWVMNBA3WSHUXPM7XKWJVRMPW6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WWVMNBA3WSHUXPM7XKWJVRMPW6","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":"b4131565a72a101859ff8474dfc3ad5f7c8f2085a39bfeb4dfcbab5339c8cc15","cross_cats_sorted":["math-ph","math.CA","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-11T10:56:46Z","title_canon_sha256":"752272ab987415103001af889c60dbb02d79267235f3c32339ccfb4ef4cfd486"},"schema_version":"1.0","source":{"id":"1301.2449","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2449","created_at":"2026-05-18T02:32:14Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2449v3","created_at":"2026-05-18T02:32:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2449","created_at":"2026-05-18T02:32:14Z"},{"alias_kind":"pith_short_12","alias_value":"WWVMNBA3WSHU","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WWVMNBA3WSHUXPM7","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WWVMNBA3","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:008068867be74a8b1ec62ef29cd8b21db8cfc365c512cf5ac90f799314a46e3a","target":"graph","created_at":"2026-05-18T02:32:14Z","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 prove the complete monotonicity on $(0,\\infty)^n$ for suitable inverse powers of the spanning-tree polynomials of graphs and, more generally, of the basis generating polynomials of certain classes of matroids. This generalizes a result of Szego and answers, among other things, a long-standing question of Lewy and Askey concerning the positivity of Taylor coefficients for certain rational functions. Our proofs are based on two_ab initio_ methods for proving that $P^{-\\beta}$ is completely monotone on a convex cone $C$: the determinantal method and the quadratic-form method. These methods are","authors_text":"Alan D. Sokal, Alexander D. Scott","cross_cats":["math-ph","math.CA","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-11T10:56:46Z","title":"Complete monotonicity for inverse powers of some combinatorially defined polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2449","kind":"arxiv","version":3},"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":"sha256:994d1451b49dc48e1ad30258e241d27c237c0b8b4e6f2b5d84dee02f0e45620f","target":"record","created_at":"2026-05-18T02:32:14Z","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":"b4131565a72a101859ff8474dfc3ad5f7c8f2085a39bfeb4dfcbab5339c8cc15","cross_cats_sorted":["math-ph","math.CA","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-11T10:56:46Z","title_canon_sha256":"752272ab987415103001af889c60dbb02d79267235f3c32339ccfb4ef4cfd486"},"schema_version":"1.0","source":{"id":"1301.2449","kind":"arxiv","version":3}},"canonical_sha256":"b5aac6841bb48f4bbd9fbaac9ac58fb792d4ae8b7cf595c35f8a87f8b3f663dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5aac6841bb48f4bbd9fbaac9ac58fb792d4ae8b7cf595c35f8a87f8b3f663dc","first_computed_at":"2026-05-18T02:32:14.560843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:14.560843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Ifm+/6S0U2daLHc9MvGU3Qx9uZIwgGMMV/s0AnOTQHlZq2ptkNXrYwWk3DJgxZHYW44AG9YW6gK2obEDriNDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:14.561503Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2449","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:994d1451b49dc48e1ad30258e241d27c237c0b8b4e6f2b5d84dee02f0e45620f","sha256:008068867be74a8b1ec62ef29cd8b21db8cfc365c512cf5ac90f799314a46e3a"],"state_sha256":"fca5140b624523ba5d14cad2341090097330e30ba7b732048381baf9b6a0c1ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nxF6y/+2+JVlTZtV0Ls3d4JuOWXHNp8uVHk/hAVj93F1NAwGwPX1iZ+0D1VHypagD7A6ksjfrqmxZehwpKMDBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T15:19:05.372260Z","bundle_sha256":"c826e81ddbc88c067105b2bb35c29829efa2cd061e87154df87f59bbc01be3b3"}}